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Interdisciplinary research on potential analysis

Research Project

Project/Area Number 11304008
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionShimane University

Principal Investigator

SUGIE Jitsuro  Shimane Univ., Dept. of Math. Professor, 総合理工学部, 教授 (40196720)

Co-Investigator(Kenkyū-buntansha) MIZUTA Yoshihiro  Hiroshima Univ., Dept. of Math. Professor, 総合科学部, 教授 (00093815)
YAMASAKI Maretsugu  Shimane Univ., Dept. of Math. Professor, 総合理工学部, 教授 (70032935)
AIKAWA Hiroaki  Shimane Univ., Dept. of Math. Professor, 総合理工学部, 教授 (20137889)
HARA Tadayuki  Osaka Pref. Univ., Dept. of Math. Professor, 工学部, 教授 (20029565)
MURATA Minoru  Tokyo Inst. Tech., Dept. of Math. Professor, 理学部, 教授 (50087079)
福島 正俊  関西大学, 工学部, 教授 (90015503)
酒井 良  東京都立大学, 理学部, 教授 (70016129)
Project Period (FY) 1999 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥38,510,000 (Direct Cost: ¥33,800,000、Indirect Cost: ¥4,710,000)
Fiscal Year 2002: ¥10,660,000 (Direct Cost: ¥8,200,000、Indirect Cost: ¥2,460,000)
Fiscal Year 2001: ¥9,750,000 (Direct Cost: ¥7,500,000、Indirect Cost: ¥2,250,000)
Fiscal Year 2000: ¥8,200,000 (Direct Cost: ¥8,200,000)
Fiscal Year 1999: ¥9,900,000 (Direct Cost: ¥9,900,000)
Keywordsseparatrix / limit cycle / homoclinic orbit / Lie^^'nard system / Euler equation / self-adjoint equation / elliptic equation / positive solution / Dirichlet解 / 調和関数 / 熱方程式 / 確率過程 / 時間遅れをもつ方程式 / 境界値 / 漸近挙動 / 整関数 / ポテンシャル / 調和 / 優調和 / ソボレフ関数 / 境界条件 / 放物型 / 非線型 / 可積分性 / Carleson測度 / 調和測度 / Network / Markov過程
Research Abstract

Van der Pol's equation was formulated to describe relaxation oscillations in electrical circuits, and played an important role in development of the theory of nonlinear oscillations and the theory of Hopf bifurcation. It is well-known that this equation has exactly one limit cycle with two unbounded separatrices. Although the separatrices are closely related to the limit cycle, little is known about the position of separatrices. In this research, we estimate the position by use of phase plane analysis and some Liapunov functions. Also, we consider the Lie^^'nard system which is a generalization of van del Pol's equation and give some conditions under which the Lie^^'nard system has homoclinic orbits.
We deal with the oscillation problem for various differential equations of Euler type and nonlinear self-adjoint differential equations, and present necessary and sufficient conditions for all nontrivial solutions to be oscillatory. The obtained theorems extend many previous results on this problem. We also discuss whether all solutions of nonlinear differential equations with time delay (or with decaying coefficients) oscillate or not. Changing variables, we can rewrite those equations into systems of Lie^^'nard type. For this reason, by means of phase plane analysis of the systems, we can examine the asymptotic behaviour of solutions in detail.
Combining the above results and the so-called "supersolution-subsolution method", we obtain sufficient conditions for quasilinear elliptic equations (or Schro^^<..>dinger equations) to have a positive solution which decays at infinity.

Report

(5 results)
  • 2002 Annual Research Report   Final Research Report Summary
  • 2001 Annual Research Report
  • 2000 Annual Research Report
  • 1999 Annual Research Report
  • Research Products

    (252 results)

All Other

All Publications (252 results)

  • [Publications] J.Sugie, M.Katayama: "Global asymptotic stability of a predator-prey system of Holling type"Nonlinear Anal.. 38. 105-121 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] J.Sugie, K.Kita: "Oscillation criteria for second order nonlinear differential equations of Euler type"数理解析研究所講究録「数理モデルと関数方程式」. 1128. 77-81 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] J.Sugie: "A nonoscillation theorem for second order nonlinear differential equations with decaying coefficients"数理解析研究所講究録「数理モデルと関数方程式」. 1128. 91-100 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] J.Sugie: "Uniqueness of limit cycles in a predator-prey system of Holling-type functional response"Quart. Appl. Math.. 58. 577-590 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] J.Sugie, M.Iwasaki: "Oscillation of the Riemann-Weber version of Euler differential equations with delay"Georgian Math. J.. 7. 577-584 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] J.Sugie: "Lienard dynamics with an open limit orbit"NoDEA Nonlinear Differential Equations Appl.. 8. 83-97 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] J.Sugie: "A nonoscillation theorem for second-order nonlinear differential equations with decaying coefficients"Bull. London Math. Soc.. 33. 299-308 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] J.Sugie, K.Kita: "Oscillation criteria for second order nonlinear differential equations of Euler type"J. Math. Anal. Appl.. 253. 414-439 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] J.Sugie, N.Yamaoka, Y.Obata: "Nonoscillation theorems for a nonlinear self-adjoint differential equations"Nonlinear Anal.. 47. 4433-4444 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] J.Sugie, N.Yamaoka: "Nonosciallation theorems for second order nonlinear differential equations of Euler type"数理解析研究所講究録「関数方程式の定性的理論とその現象解析への応用」. 1216. 224-235 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] J.Sugie: "On the position of unbounded separatrices for van der Pol's system"Dynamics Systems Appl.. 11. 53-63 (2002)

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      「研究成果報告書概要(和文)」より
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      2002 Final Research Report Summary
  • [Publications] J.Sugie, K.Kita, N.Yamaoka: "Oscillation constant of second-order non-linear self-adjoint differential equations"Ann. Mat. Pura Appl.(4). 181. 309-337 (2002)

    • Description
      「研究成果報告書概要(和文)」より
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      2002 Final Research Report Summary
  • [Publications] J.Sugie, N.Yamaoka: "An infinite sequence of nonoscillation theorems for second-order nonlinear differential equations of Euler type"Nonlinear Anal.. 50. 373-388 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] J.Sugie, N.Yamaoka: "Decaying positive solutions of quasilinear elliptic equations in exterior domains in R^2"J.Math.Anal.Appl.. 275. 288-311 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] J.Sugie, N.Yamaoka: "Applications of phase plane analysis of a Lienard system to positive solutions of Schrodinger equations"数理解析研究所講究録「関数方程式の解のダイナミクスとその周辺」. 1254. 132-141 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] J.Sugie, N.Yamaoka: "Applications of phase plane analysis of a Lienard system to positive solutions of Schrodinger equations"Proc. Amer. Math. Soc.. 131. 501-509 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] J.Sugie: "Oscillation criteria of Kneser-Hille type for second-order differential equations with nonlinear perturbed terms"Rocky Mountain J. Math.. (to appear). (2003)

    • Description
      「研究成果報告書概要(和文)」より
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      2002 Final Research Report Summary
  • [Publications] H.Aikawa, M.Ohtsuka: "Extremal length of vector measures"Ann. Acad. Sci. Fenn. Math.. 24. 61-88 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H.Aikawa, T.Mizutani: "Martin boundary for a uniformly John domain"数理解析研究所講究録「ポテンシャル論とその関連分野」. 1116. 11-28 (1999)

    • Description
      「研究成果報告書概要(和文)」より
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      2002 Final Research Report Summary
  • [Publications] H.Aikawa, S.J.Gardiner: "Evaluation of superharmonic functions using limits along lines"Bull. London. Math. Soc.. 32. 209-213 (2000)

    • Description
      「研究成果報告書概要(和文)」より
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      2002 Final Research Report Summary
  • [Publications] H.Aikawa: "Integrability of superharmonic functions in a John domain"Proc. Amer. Math. Soc.. 128. 195-201 (2000)

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      2002 Final Research Report Summary
  • [Publications] H.Aikawa: "Boundary Harnack principle and Martin boundary for a uniform domain"J. Math. Soc. Japan. 53. 119-145 (2001)

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      2002 Final Research Report Summary
  • [Publications] H.Aikawa: "Holder continuity of the Dirichlet solution for a general domain"Bull. London Math. Soc.. 34. 691-702 (2002)

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      2002 Final Research Report Summary
  • [Publications] H.Aikawa, K.Hirata, T.Lundh: "Martin boundary for union of convex sets"数理解析研究所講究録「ポテンシャル論とその周辺」. 1293. 1-14 (2002)

    • Description
      「研究成果報告書概要(和文)」より
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      2002 Final Research Report Summary
  • [Publications] 相川弘明: "複雑領域のMartin境界と境界Harnack原理"数学. 55. 1-19 (2003)

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      「研究成果報告書概要(和文)」より
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      2002 Final Research Report Summary
  • [Publications] H.Aikawa, T.Lundh, t.Mizutani: "Martin boundary of a fractal domain"Potential Anal.. (to appear). (2003)

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      「研究成果報告書概要(和文)」より
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      2002 Final Research Report Summary
  • [Publications] H.Aikawa: "Positive harmonic functions of finite order in a Denjoy-type domain"Proc. Amer. Math. Soc.. (to appear). (2003)

    • Description
      「研究成果報告書概要(和文)」より
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      2002 Final Research Report Summary
  • [Publications] M.Yamasaki: "Inequalities on networks"数理解析研究所講究録「最適化のための連続と離散数理」. 1114. 184-193 (1999)

    • Description
      「研究成果報告書概要(和文)」より
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      2002 Final Research Report Summary
  • [Publications] Y.Shogenji, M.Yamasaki: "Hardy's inequality on finite networks"Mem. Fac. Sci. Eng. Shimane Univ. Ser. B. Math. Sci.. 32. 75-84 (1999)

    • Description
      「研究成果報告書概要(和文)」より
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      2002 Final Research Report Summary
  • [Publications] W.Oetti, M.Yamasaki: "Duality theorems on an infinite networks"Optimization. 48. 1-15 (2000)

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      「研究成果報告書概要(和文)」より
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      2002 Final Research Report Summary
  • [Publications] A.Murakami, M.Yamasaki: "Inequalities on infinite networks"Mem. Fac. Sci. Eng. Shimane Univ. Ser. B. Math. Sci.. 33. 47-62 (2000)

    • Description
      「研究成果報告書概要(和文)」より
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      2002 Final Research Report Summary
  • [Publications] A.Murakami, M.Yamasaki: "A weighted Sobolev-Poincare's inequality on infinite networks"Mem. Fac. Sci. Eng. Shimane Univ. Ser. B. Math. Sci.. 34. 45-52 (2001)

    • Description
      「研究成果報告書概要(和文)」より
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      2002 Final Research Report Summary
  • [Publications] X.Chen, Y.Shogenji, M.Yamasaki: "Verification for existence of solution of linear complementarity problems"Linear Algebra Appl.. 324. 15-26 (2001)

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      「研究成果報告書概要(和文)」より
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      2002 Final Research Report Summary
  • [Publications] Y.Mizuta: "Multiple exponential integrability for Riesz potential of functions in Orlicz classes"Advances in Math. Sci. Appl.. 9. 621-631 (1999)

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      2002 Final Research Report Summary
  • [Publications] Y.Mizuta, T.Shimomura: "Boundary limits of spherical means for BLD and monotone BLD functions in the unit ball"Acad. Sci. Fenn. Ser. A. I. Math.. 24. 45-60 (1999)

    • Description
      「研究成果報告書概要(和文)」より
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      2002 Final Research Report Summary
  • [Publications] Y.Mizuta, T.Shimomura: "Growth properties of spherical means for monotone BLD functions in the unit ball"Acad. Sci. Fenn. Ser. A. I. Math.. 25. 457-465 (2000)

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      「研究成果報告書概要(和文)」より
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      2002 Final Research Report Summary
  • [Publications] Y.Mizuta, T.Shimomura: "Differentiability and Holder continuity of Riesz potential of functions in Orlicz classes"Analysis. 20. 201-223 (2000)

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      「研究成果報告書概要(和文)」より
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      2002 Final Research Report Summary
  • [Publications] T.Futamura, K.Kishi, Y.Mizuta: "A generalization of the Liouville theorem to polyharmonic functions"J. Math. Soc. Japan. 53. 113-118 (2001)

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      2002 Final Research Report Summary
  • [Publications] T.Futamura, K.Kishi, Y.Mizuta: "A generalization of Bocher's theorem for polyharmonic functions"Hiroshima Math. J.. 31. 59-70 (2001)

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      「研究成果報告書概要(和文)」より
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      2002 Final Research Report Summary
  • [Publications] T.Futamura, Y.Mizuta: "Existence of functions in weighted Sobolev spaces"Nagoya Math. J.. 164. 75-88 (2001)

    • Description
      「研究成果報告書概要(和文)」より
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      2002 Final Research Report Summary
  • [Publications] Y.Mizuta, T.Shimomura: "Holder continuity and differentiability for weighted Sobolev spaces"Proc. Amer. Math. Soc.. 130. 2985-2994 (2002)

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      2002 Final Research Report Summary
  • [Publications] T.Futamura, K.Kishi, Y.Mizuta: "Removability of sets for subpolyharmonic functions"Hiroshima Math J.. (to appear). (2003)

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      2002 Final Research Report Summary
  • [Publications] T.Futamura, Y.Mizuta: "Tangential limits and removable sets for weighted Sobolev spaces"Hiroshima Math J.. (to appear). (2003)

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      2002 Final Research Report Summary
  • [Publications] K.Ishige, M.Murata: "Uniqueness of nonnegative solutions of the Cauchy problem for parabolic equations on manifolds or domains"Ann.Scuola Norm. Sup. Pisa Cl. Sci.(4). 30. 171-223 (2001)

    • Description
      「研究成果報告書概要(和文)」より
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      2002 Final Research Report Summary
  • [Publications] M.Murata: "Martin boundaries of elliptic skew products, semismall perturbations, and foundamental solutions of parabolic equations"J. Funct. Anal.. 194. 53-141 (2002)

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      2002 Final Research Report Summary
  • [Publications] M.Murata, T.Tsuchida: "Asymptotic of Green functions and Martin boundaries for elliptic operators with periodic coefficients"数理解析研究所講究録「スペクトル・散乱理論とその周辺」. 1255. 103-123 (2002)

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      2002 Final Research Report Summary
  • [Publications] M.Murata: "Heat escape"Math. Ann.. (to appear). (2003)

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      2002 Final Research Report Summary
  • [Publications] H.Matsunaga, R.Miyazaki, T.Hara: "Global attractivity results for nonlinear delay differential equations"J. Math. Anal. Appl.. 234. 77-90 (1999)

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      2002 Final Research Report Summary
  • [Publications] H.Matsunaga, T.Hara: "The asymptotic stability of a two-dimentional linear delay difference equation"Dynam. Contin. Discrete Impuls. Syst.. 6. 465-473 (1999)

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      2002 Final Research Report Summary
  • [Publications] Y.Saito, T.Hara, W.Ma: "Necessary and sufficient condisions for permanence and global stability of a Lotka-Volterra system with two delays"J. Math. Anal. Appl.. 236. 534-556 (1999)

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      「研究成果報告書概要(和文)」より
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      2002 Final Research Report Summary
  • [Publications] T.Hara, R.Miyazaki, T.Morii: "Asymptotic periodic solutions for linear differential-difference equations with N delays and Hopf bifurcation"Funkcial. Ekvac.. 43. 193-212 (2000)

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      2002 Final Research Report Summary
  • [Publications] W.Ma, T.Hara, Y.Takeuchi: "Stability of a 2-dimensional neural network with time delays"J.Biol. Syst.. 8. 177-193 (2000)

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      2002 Final Research Report Summary
  • [Publications] R.Ogita, H.Matsunaga, T.Hara: "Asymptotic stability condition for a class of linear delay difference equations of higher order"J. Math. Anal. Appl.. 248. 83-96 (2000)

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      2002 Final Research Report Summary
  • [Publications] S.Skata, T.Hara: "Dynamics of a linear differential system with piecewise constant argument"Dynam. Contin. Discrete Impuls. Syst.. 7. 585-594 (2000)

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      2002 Final Research Report Summary
  • [Publications] T.Hara, S.Skata: "Dynamics of a delay differential system with periodically oscillation coefficients"Nonlinear Anal.. 47. 4399-4408 (2001)

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  • [Publications] E.Beretta, T.Hara, et al.: "Global asymptotic stability of an SIR epidemic model with distributed time delay"Nonlinear Anal.. 47. 4107-4115 (2001)

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      2002 Final Research Report Summary
  • [Publications] Y.Saito, W.Ma, T.Hara: "A necessary and sufficient condition for permanence of a Lotka-Volterra discrete system with delays"J. Math. Anal. Appl.. 256. 162-174 (2001)

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      「研究成果報告書概要(和文)」より
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      2002 Final Research Report Summary
  • [Publications] H.Matsunaga, T.Hara, S.Skata: "Global attractivity for a nonlinear difference equation with variable delay"Comput. Math. Appl.. 41. 543-551 (2001)

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      「研究成果報告書概要(和文)」より
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      2002 Final Research Report Summary
  • [Publications] H.Matsunaga, T.Hara, S.Skata: "Global attractivity for a logistic equation with piecewise constant argument"NoDEA Nonlinear Differential Equations Appl.. 8. 45-52 (2001)

    • Description
      「研究成果報告書概要(和文)」より
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      2002 Final Research Report Summary
  • [Publications] T.Hara, S.Skata: "Star-shaped periodic solutions for x'(t)=-α{1-‖x(t)‖^2}R(θ)x([t])"Nonlinear Anal.. 49. 455-470 (2002)

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      「研究成果報告書概要(和文)」より
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      2002 Final Research Report Summary
  • [Publications] Y.Saito, T.Hara, W.Ma: "Harmless delays for permanence and impersistence of a Lotka-Volterra discrete predator-prey system"Nonlinear Anal.. 50. 703-715 (2002)

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      2002 Final Research Report Summary
  • [Publications] W.Ma, Y.Takeuchi, T.Hara et al.: "Permanence of an SIR epidemic model with distributed time delays"Tohoku Math. J.. 54. 581-591 (2002)

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      「研究成果報告書概要(和文)」より
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      2002 Final Research Report Summary
  • [Publications] 相川弘明(編集): "数理解析研究所講究録「ポテンシャル論とその周辺」1293"京都大学数理解析研究所. 198 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] J,Sugie., M,Katayama.: "Global asymptotic stability of a predator-prey system of Holling type"Nonlinear Anal. 38. 105-121 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] J,Sugie., K,Kita.: "Oscillation criteria for second order nonlinear differential equations of Euler type"RIMS Kokyukoku. 1128. 77-81 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] j,Sugie.: "A nonoscillation theorem for second order nonlinear differential equations with decaying coefficients"RIMS Kokyukoku. 1128. 91-100 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] j,Sugie.: "Uniqueness of limit cycles in a predator-prey system with Holling-type functional response"Quart. Appl. Math.. 58, 3. 577-590 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] j,Sugie., M,Iwasaki.: "Oscillation of the Riemann-Weber version of Euler differential equations with delay"Georgian Math. J.. 7. 577-584 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] j,Sugie.: "Lie^^'nard dynamics with an open limit orbit"NoDEA Nonlinear Differential Equations Appl.. 8. 83-97 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] j,Sugie.: "A nonoscillation theorem for second-order nonlinear differential equations with decaying coefficients"Bull. London Math. Soc.. 33. 299-308 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] j,Sugie., K,Kita.: "Oscillation criteria for second order nonlinear differential equations of Euler type"J. Math. Anal. Appl.. 253. 414-439 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] j,Sugie., N,Yamaoka., Y,Obata.: "Nonoscillation theorem for a nonlinear self-adjoint differential equation"Nonlinear Anal.. 47. 4433-4444 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] j,Sugie., N,Yamaoka.: "Nonoscillation theorems for second order nonlinear differential equations of Euler type"RIMS Kokyukoku. 1216. 224-235 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] j,Sugie.: "On the position of unbounded separatrices for van der Pol's system"Dynam. Systems Appl.. 11. 53-63 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] J.Sugie., K,Kita., N,Yamaoka.: "Oscillation constant of second-order non-linear selfadjoint differential equations"Ann. Mat. Pura Appl.(4). 181. 309-337 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] J.Sugie., N,Yamaoka.: "An infinite sequence of nonoscillation theorems for second-order nonlinear differential equations of Euler type"Nonlinear Anal.. 50. 373-388 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] J.Sugie., N,Yamaoka.: "Decaying positive solutions of quasilinear elliptic equations in exterior domains in R^2"J. Math. Anal.. 275. 288-311 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] J.Sugie., N,Yamaoka.: "Applications of phase plane analysis of a Lie^^'nard system to positive solutions of Schro^^..dinger equations"RIMS Kokyukoku. 1254. 132-141 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] J.Sugie., N,Yamaoka.: "Applications of phase plane analysis of a Lie^^'nard system to positive solutions of Schr^^<..>dinger equations"Proc. Amer. Math. Soc.. 131. 501-509 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] J.Sugie.: "Oscillation criteria of Kneser-Hille type for second-order differential equations with nonlinear perturbed terms"Rocky Mountain J. Math., (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H,Aikawa., M,Ohtsuka.: "Extremal length of vector measures"Ann. Acad. Sci. Fenn. Math.. 24. 61-88 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H,Aikawa., T,Mizutani.: "Martin boundary for a uniformly John domain"RIMS Kokyukoku. 1116. 11-28 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H,Aikawa., S.J.Gardiner.: "Evaluation of superharmonic functions using limits along lines"Bull. London Math. Soc.. 32. 209-213 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H,Aikawa.: "Integrability of superharmonic functions in a John domain"Proc. Amer. Math. Soc.. 128. 195-201 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H,Aikawa.: "Boundary Harnack principle and Martin boundary for a uniform domain"J. Math. Soc. Japan. 53. 119-145 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H,Aikawa.: "Ho^^<..>lder continuity of the Dirichlet solution for a general domain"Bull. London Math. Soc.. 34. 691-702 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H,Aikawa., K,Hirata., T,Lundh.: "Martin boundary for union of convex sets"RIMS Kokyukoku. 1293. 1-14 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H,Aikawa.: "Martin boundary and boundary Harnack principle for nonsmooth domains"Sugaku. 55. 1-19 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H,Aikawa., T,Lundh., T,Mizutani: "Martin boundary of a fractal domain"Potential Anal. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H,Aikawa.: "Positive harmonic functions of finite order in Denjoy-type domain"Proc. Amer. Math. Soc., (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M,Yamasaki.: "Inequalities on networks"RIMS Kokyukoku. 1114. 184-193 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y,Shoenji., M,Yamasaki.: "Hardy's inequality on finite networks"Mem. Fac. Sci. Eng. Shimane Univ. Ser. B. Math. Sci.. 32. 75-84 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] W,Oettlli., M,Yamasaki.: "Duality theorems on an infinite networks"Optimization. 48. 1-15 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] A,Murakami., M,Yamasaki.: "Inequalities on infinite networks"Mem. Fac. Sci. Eng. Shimane Univ. Ser. B. Math. Sci.. 33. 47-62 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] A,Murakami., M,Yamasaki.: "A weighted Sobolev-Poincare^^''s inequality on infinite networks"Mem. Fac. Sci. Eng. Shimane Univ. Ser. B. Math. Sci.. 34. 45-52 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] X,Chen., Y,Shogenji., M,Yamasaki.: "Verification for existence of solutions of linear complementarity problems"Linear Algebra Appl.. 324. 15-26 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y,Mizuta.: "Multiple exponential integrability for Riesz potential of function in Orlicz Classes"Advances in Math. Sci. Appl.. 9. 621-631 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y,Mizuta., T,Shimomura.: "Boundary limits of spherical means for BLD and monotone BLD functions in the unit ball"Acad. Sci. Fenn. Ser. A. I. Math.. 24. 45-60 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y,Mizuta., T,Shimomura.: "Growth properties of spherical means for monotone BLD functions in the unit ball"Acad. Sci. Fenn. Ser. A. I. Math.. 25. 457-465 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y,Mizuta., T,Shimomura.: "Differentiability and Ho^^<..>lder continuity of Riesz potentials of functions in Orlicz classes"Analysis. 20. 201-223 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T,Futamura., K,Kishi., Y,Mizuta.: "A generalization of the Liouville theorem to polyharmonic functions"J. Math. Soc. Japan. 53. 113-118 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T,Futamura., K,Kishi., Y,Mizuta.: "A generalization of the Bo^^^cher's theorem for polyharmonic functions"Hiroshima Math. J.. 31. 59-70 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T,Futamura., Y,Mizuta.: "Existence of functions in weighted Sobolev spaces"Nagoya Math. J.. 164. 75-88 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y,Mizuta., T,Shimomura.: "Ho^^<..>lder continuity and differentiability for weighted Sobolev spaces"Proc. Amer. Math. Soc.. 130. 2985-2994 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T,Futamura., K,Kishi., Y,Mizuta.: "Remonvability of sets for subpolyharmonic functions"Hiroshima Math. J., (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T,Futamura., Y,Mizuta.: "Tangential limits and removable sets for weighted Sobolev spaces"Hiroshima Math. J., (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K,Ishige., M,Murata.: "Uniqueness of nonnegative solutions of the Cauchy problem for parabolic equations on manifolds or domains"Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4). 30. 171-223 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M,Murata.: "Martin boundaries of elliptic skew products, semismall perturbations, and foundamental solutions of parabolic equations"J. Funct. Anal.. 194. 53-141 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M,Murata., T,Tsuchida.: "Asymptotic of Green functions and Martin boundaries of elliptic operators with periodic coefficients"RIMS Kokyukoku. 1255. 103-123 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M,Murata.: "Heat escape"Math. Ann., (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H,Matsunaga., R,Miyazaki., T,Hara.: "Global attractivity results for nonlinear delay differential equations"J. Math. Anal. Appl.. 234. 77-90 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H,Matsunaga., T,Hara.: "The asymptotic stability of a two-dimensional linear delay difference equation"Dynam. Cotin. Discrete Impuls. Syst.. 6. 465-473 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y,Saito., T,Hara., W,Ma.: "Necessary and sufficient conditions for permanence and global stability of a Lotka-Volterra system with two delays"J. Math. Anal. Appl.. 236. 534-556 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T,Hara., R,Miyazaki., T,Morii.: "Asymptotic periodic solutions for linear differential-difference equations with N delays and Hopf bifurcation"Funkcial. Ekvac.. 43. 193-212 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] W,Ma., T,Hara., Y,Takeuchi.: "Stability of a 2-dimensional neural network with time delays"J. Biol. Syst.. 8. 177-193 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] R,Ogita., H,Matsunaga., T,Hara.: "Asymptotic stability condition for a class of linear delay difference equations of higher order"J. Math. Anal.. 248. 83-96 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S,Sakata., T,Hara.: "Dynamics of a linear differential system with piecewise constant argument"Dynam. Contin. Discrete Impuls. Syst.. 7. 585-594 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T,Hara., S,Sakata.: "Dynamics of a delay differential system with perodically oscillatory coefficients"Nonlinear Anal.. 47. 4399-4408 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] E,Beretta., T,Hara., W,Ma., Y,Takeuchi.: "Global asymptotic stability of an SIR epidemic model with distributed time delay"Nonlinear Anal.. 47. 4107-4115 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y,Saito., W,Ma., T,Hara.: "A necessary and sufficient condition for permanence of a Lotka-Volterra discrete system with delays"J. Math. Anal. Appl.. 256. 162-174 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H,Matsunaga., T,Hara., S,Sakata.: "Global attractivity for a nonlinear difference equation with variable delay"Comput. Math. Appl.. 41. 543-551 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H,Matsunaga., T,Hara., S,Sakata.: "Global attractivity for a logistic equation with piecewise constant argument"NoDEA Nonlinear Differential Equations Appl.. 8. 45-52 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T,Hara., S,Sakata.: "Star-shaped periodic solutions for x'(t)=-α{1-||x(t)||^2}R(θ)x([t])"Nonlinear Anal.. 49. 455-470 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y,Saito., T,Hara., W,Ma.: "Harmless delays for permanence and impersistence of a Lotka-Volterra discrete predator-prey system"Nonlinear Anal.. 50. 703-715 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] W,Ma., Y,Takeuchi., T,Hara., E,Beretta.: "Permanence of an SIR epidemic model with distributed time delays"To^^^hoku Math. J.. 54. 581-591 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] J.Sugie: "On the position of unbounded separatrices for van der Pol's system"Dynamic Systems Appl.. 11. 53-63 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] J.Sugie, K.Kita, N.Yamaoka: "Oscillation constant of second-order non-linear self-adjoint differential equations"Ann. Mat. Pura Appl.(4). 181. 309-337 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] J.Sugie, N.Yamaoka: "An infinite sequence of nonoscillation theorems for second-order nonlinea differential equations of Euler type"Nonlinear Anal.. 50. 373-388 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] J.Sugiem N.Yamaoka: "Decaying positive solutions of quasilinear elliptic equations in exterior domains in R^2"J. Math. Anal. Appl.. 275. 288-311 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] J.Sugie, N.Yamaoka: "Applications of phase plane analysis of a Lienard system to positive solution of Schrodinger equations"Proc. Amer. Math. Soc.. 131. 501-509 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] J.Sugie: "Oscillation criteria of Kneser-Hille type for second-order differential equations with nonlinear perturbed terms"Rocky Mountain J.Math.. (to appear).

    • Related Report
      2002 Annual Research Report
  • [Publications] J.Sugie, N.Yamaoka: "Applications of phase plane analysis of a Lienard system to positive solutions of Schrodinger equations"数理解析研究所講究録「関数方程式の解のダイナミクスとその周辺」. 1254. 132-141 (2002)

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      2002 Annual Research Report
  • [Publications] H.Aikawa: "Holder continuity of the Dirichlet solution for a general domain"Bull. London Math. Soc.. 34. 691-702 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] H.Aikawa, K.Hirata, T.Lundh: "Martin boundary for union of convex sets"数理解析研究所講究録「ポテンシャル論とその周辺」. 1293. 1-14 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 相川弘明: "複雑領域のMartin境界と境界Harnack原理"数学. 55. 1-19 (2003)

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      2002 Annual Research Report
  • [Publications] H.Aikawa, T.Lundh, T.Mizutani: "Martin boundary of a fractal domain"Potential Anal.. (to appear). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] H.Aikawa: "Positive harmonic functions of finite order in a Denjoy type domain"Proc. Amer. Math. Soc.. (to appear). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Mizuta, T.Shimomura: "Holder continuity and differentiability for weighted Sobolev spaces"Proc. Amer. Math. Soc.. 130. 2985-2994 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Futamura, K.Kishi, Y.Mizuta: "Removability of sets for subpolyharmonic functions"Hiroshima Math J.. (to appear). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Futamura, Y.Mizuta: "Tangential limits and removable sets for weighted Sobolev spaces"Hiroshima Math J.. (to appear). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] M.Murata: "Martin boundaries of elliptic skew products, semismall perturbations, and foundamental solutions of parabolic equations"J. Funct. Anal.. 194. 53-141 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] M.Murata, T.Tsuchida: "Asymptotic of Green functions and Martin Martin boundaries for elliptic operators with periodic coefficients"数理解析研究所講究録「スペクトル・散乱理論とその周辺」. 1255. 103-123 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] M.Murata: "Heat escape"Math. Ann.. (to appear). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Hara, S.Skata: "Star-shaped periodic solutions for x'(t)=-α{1-llx(t)ll^2}R(θ)x([t])"Nonlinear Anal.. 49. 455-470 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Saito, T.Hara, W.Ma: "Harmless delays for permanence and impersistence of a Lotka-Volterra discrete predator-prey system"Nonlinear Anal.. 50. 703-715 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] W.Ma, Y.Takeuchi, T.Hara, et al.: "Permanence of an SIR epidemic model with distributed time delays"Tohoku Math. J.. 54. 581-591 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 相川弘明(編集): "数理解析研究所講究録「ポテンシシャル論とその周辺」1293"京都大学数理解析研究所. 198 (2002)

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      2002 Annual Research Report
  • [Publications] J.Sugie, K.Kita: "Oscillation criteria for second order nonlinear differential equations of Euler type"J. Math. Anal. Appl.. 253. 414-439 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] J.Sugie: "Lienard dynamics with an open limit orbit"NoDEA Nonlinear Differential Equations Appl.. 8. 83-97 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] J.Sugie: "A nonoscillation theorem for second order nonlinear differential equations with decaying coefficients"Bull. London Math. Soc.. 33. 299-308 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] J.Sugie, N.Yamaoka, Y.Obata: "Nonoscillation theorems for a nonlinear self-adjoint differential equation"Nonlinear Anal.. 47. 4433-4444 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] J.Sugie, N.Yamaoka: "An infinite sequence of nonoscillation theorems for second order nonlinear differential equations of Euler type"Nonlinear Anal.. (to appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] J.Sugie, K.Kita, N.Yamaoka: "Oscillation constant of second order nonlinear seif-adjoint differential equations"Ann. Mat. Pura Appl.. (to appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] J.Sugie, N.Yamaoka: "Applications of phase plane analysis of a Lienard system to positive solutions of Schrodinger equations"Proc. Amer. Math. Soc.. (to appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] J.Sugie, N.Yamaoka: "Nonoscillation theorems for second order nonlinear differential equations of Euler type"数理解析研究所講究録. 1216. 224-235 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] H.Aikawa: "Holder continuity of Dirichiet solution for a general domain"Bull. London Math. Soc.. (to appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] T.A.Burton, T.Furumochi: "Fixed points and problems in stability theory for ordinary and functional differential equations"Dynamic Systems and Applications. 10. 89-116 (2001)

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      2001 Annual Research Report
  • [Publications] T.A.Burton, T.Furumochi: "A note on stability by Schauder's theorem"Funkcialaj Ekvacioj. 44. 73-82 (2001)

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      2001 Annual Research Report
  • [Publications] T.Furumochi: "Periodic solutions of Volterra difference equations and attractivity"Nonlinear Analysis. 44. 4013-4024 (2001)

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      2001 Annual Research Report
  • [Publications] T.Futamura, K.Kishi, Y.Mizuta: "A generalization of the Liouville theorem to polyharmonic functions"J. Math. Soc. Japan. 53. 113-118 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] T.Futamura, K.Kishi, Y.Mizuta: "A generalization of Bocher's theorem for polyharmonic functions"Hiroshima Math. J.. 31. 59-70 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] T.Futamura.Y.Mizuta: "Existence of functions in weighted Sobolev spaces"Nagoya Math. J.. 164. 75-88 (2001)

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      2001 Annual Research Report
  • [Publications] Y.Mizuta: "Boundary limits of functions in weighted Lebesgue or Sobolev classes"Revue Roumaine Math. Pures Appl.. 46. 67-75 (2001)

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      2001 Annual Research Report
  • [Publications] H.Arai: "Hardy spaces, Carleson measures and a gradient estimate for harmonic functions on negatively curved manifolds"Advanced Studies in Pure Mathematics. 31. 1-49 (2001)

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      2001 Annual Research Report
  • [Publications] N.Suzuki, N.A.Watson: "A characterization of heat balls by a mean value property for temperatures"Proc. Amer. Math. Soc.. 129. 2709-2713 (2001)

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      2001 Annual Research Report
  • [Publications] H.Sato: "Jorgensen's inequality for classical Schottky groups of real type, II"J. Math. Soc. Japan. 53. 791-811 (2001)

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      2001 Annual Research Report
  • [Publications] H.Sato: "The Picard group, the Whitehead link and Jorgensen groups"Proc. of the third ISAAC Congress. (to appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] M.Taniguchi: "Non-trivial deformation of an entire function abz+e^<bz>+c"Taiwan J. math.. 5. 641-646 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] M.Taniguchi: "Explicit representation of structurally finite entire functions"Proc. Japan Acad.. 77. 68-70 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] H.Morishita, E.Yanagida, S.Yotsutani: "Structural change of solutions for a scalar curvature equation"Differential and Integral Equations. 14. 273-288 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] B.Yanagida, S.Yotsutani: "A unified approach to the structure of radial solutions for semilinear elliptic problems"Japan J. Indust. Appl. Math.. 18. 503-519 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Y.Kabeya, E.Yanagida, S.Yotsutani: "Global structure of solutions for equations of Brezis-Nirenberg type on the unit ball"Proc. Roy. Soc. Edinburgh Sect. A. 131. 647-665 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] S.Yotsutani: "Canonical form related with radial solutions of semilinear elliptic equations and its applications"Taiwanese J. Math.. 5. 507-517 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Y.Kabeya, E.Yanagida, S.Yotsutani: "Canonical forms and structure theorems for radial solutions to semi-linear elliptic problems"Communication on Pure and Applied Analysis. (to appear). (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] Y.Lou, W.-M.Ni, S.Yotsutani: "On a Limiting System in the Lotka-Volterra Competition with Cross-Diffusion"Discrete and Continuous Dynamical Systems. (to appear). (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] K.Ishige.M.Murata: "Uniqueness of nonnegative solutions of the Cauchy problem for parabolic equations on manifolds or domains"Ann. Scuola Norm. Sup. Pisa. 30. 171-223 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] M.Murata: "Martin boundaries of elliptic skew products, semismall perturbations, and fundamental solutions of parabolic equations"J. Fnuc. Anal.. (to appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] Y.Hino, S.Murakami, T.Naito, N.V.Minh: "A variation-of-constants formula for abstract functional differential equations in the phase space"J. Differential Equations. (to appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] Y.Hino, S.Murakami: "Limiting equations and some stability properties for asymptotically almost periodic functional differential equations with infinite delay"Tohoku Math. J.. (to appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] Y.Hino, T.Naito, N.V.Minh, J.S.Shin: "Almost Periodic Solutions of Differential Equations in Banach Spaces"Taylor and Francis. (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] Y.Hino, S.Murakami: "Quasi-processes and stabilities in functional differential equations"Nonlinear Analysis. 47. 4025-4036 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] T.Hara, S.Sakata: "Dynamics of a delay differential system with periodically oscillatory coefficients"Nonlinear Anal.. 47. 4399-4408 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Y.Saito: "The necessary and sufficient condition for global stability of a Lotka-Volterra cooperative or competition system with delays"数理解析研究所講究録. 1216. 145-156 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] E.Beretta, T.Hara, W.Ma, Y.Takeuchi: "Global asymptotic stability of an SIR epidemic model with distributed time delay"Nonlinear Anal.. 47. 4107-4115 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] T.Hara, S.Sakata: "Stability regions for linear differential equations with two kinds of time lags"数理解析研究所講究録. 1216. 133-144 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] T.Hara, S.Sakata: "Star-shaped periodic solutions for χ(t)=-α{1-‖χ(t)‖^2}R(θ)χ([t])"Nonlinear Anal.. (to appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] H.Matsunaga, T.Hara, S.Sakata: "Global attractivity for a nonlinear difference equation with variable delay"Comput. Math. Appl.. 41. 543-551 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] H.Matsunaga, T.Hara, S.Sakata: "Global attractivity for a logistic equation with piecewise constant argument"Nonlinear Differential Equations Appl.. 8. 45-52 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] H.Matsunaga, R.Ogita, K.Murakami: "Asymptotic behavior of a system of higher order linear difference equations"Nonlinear Anal.. 47. 4667-4677 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] H.Matsunaga: "Global attractivity for nonlinear delay differential equations with impulses"数理解析研究所講究録. 1216. 128-132 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Y.Saito, W.Ma, T.Hara: "A necessary and sufficient condition for permanence of a Lotka-Volterra discrete system with delays"J. Math. Anal. Appl.. 256. 162-174 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Y.Saito, T.Hara, W.Ma: "Harmless delays for permanence and impersistence of Lotka-Volterra discrete predator-prey system"Nonlinear Anal.. (to appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] 新井 仁之: "フーリエ解析と関数解析学"培風館. 293 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] H.Aikawa: "Martin boundary of a fractal domain"Institut Mittag-Leffer, Report. 40. (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Aikawa,S.Gardinder: "Evaluation of superharmonic functions using limits along lines"Bull.London Math.Soc.. 32. 209-213 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Aikawa: "Boundary Harnack principle and Martin boundary-for a uniform domain"J.Math.Soc.Japan. 53. 119-145 (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] 新井仁之: "実解析,掛谷問題とコロナ問題-日本発の二つの問題-"数理科学. 38. 56-65 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Arai: "Singular elliptic operators related to harmonic analysis and complex analysis of several variables"Trends in Probablity and Related Analysis (World Sci.Publ.). 1-34 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Arai: "Hardy spaces, Carleson measures and a gradient estimate for harmonic functions on negatively curved manifolds"Adv.Studies in Pure Math.. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] Y.Mizuta and T.Shimomura: "Growth properties of spherical means for monotone BLD functions in the unit ball"Acad.Sci.Fenn.,Ser.A.I.Math.. 25. 457-465 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Y.Mizuta and T.Shimomura: "Differentiability and Holder continuity of Riesz potentials of functions in Orlicz classes"Analysis. 20. 201-223 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Y.Mizuta: "Boundary limits of functions in weighted Lebesgue or Sobolev classes"Revue Roumaine Math.Pures Appl.. 45(to appear). (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Futamura,K.Kishi,Y.Mizuta: "A generalization of the Liouville theorem to polyharmonic functions"J.Math.Soc.Japan. 53. 113-118 (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Futamura,K.Kishi,Y.Mizuta: "A generalization of Bocher's theorem for polyharmonic functions (to appear)"Hiroshima Math.J.. 31. (2001)

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      2000 Annual Research Report
  • [Publications] T.Futamura and Y.Mizuta: "Existence of functions in weighted Sobolev spaces (to appear)"Nagoya Math.J.. 31. (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] M.Nishio and N.Suzuki: "A charcterzation of strip domains by mean value property for the parabolic operator of order α"New Zealand J of Math.. 29. 47-54 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] N.Suzuki and N.A.Watson: "A charcterization of heat ball by mean value property for temperatures"Proc.Amer.Math.Soc.. (to appear) .

    • Related Report
      2000 Annual Research Report
  • [Publications] Oettli,W.,山崎稀嗣: "Duality theorems on an infinite network"Optimization. 48. 1-15 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 村上温,山崎稀嗣: "Inequalities on infinite networks"Mem.Fac.Sci.Shimane Univ.Ser.B : Mathematical Science. 33(to appear) . 47-62 (2000)

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      2000 Annual Research Report
  • [Publications] 陳小君,生源寺亨浩,山崎稀嗣: "Verification for existence of solutions of linear complementarity problems"Linear Algebra and Its Applications. (to appear). (2000)

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      2000 Annual Research Report
  • [Publications] 谷口雅彦: "整函数の構成:断章"数理解析研究所講究録. 1153. 103-112 (2000)

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      2000 Annual Research Report
  • [Publications] E.Fujikawa,H.Shiga and M.Taniguchi: "Discreteness of the mapping class group for Riemann surfaces of infinite analytic type"Proc.of the 2-nd ISAAC Congress. 2000. 1015-1023

    • Related Report
      2000 Annual Research Report
  • [Publications] K.Ishige and M.Murata: "Uniqueness of nonnegative solutions of the cauchy problem for parabolic equations on manifolds or domains"Ann.Scuola Normale Sup.Pisa. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Morishita,E.Yanagida,S.Yotsutani: "Structural change of solutions for a scalar curvature equation"Differential and Integral Equations. 14(to appear). (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] E.Yanagida,and S.Yotsutani: "A unified approach to the structure of radial solutions for semilinear elliptic problems"JJIAM. 18(to appear). (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Hara,R.Miyazaki,T.Morii: "Asymptotic periodic solutions for linear differential-difference equations with N delays and Hopf bifurcation"Funkcialaj Ekvacioj. 43. 193-212 (2000)

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      2000 Annual Research Report
  • [Publications] W.Ma,T.Hara,Y.Takeuchi: "Stability of a 2-dimensional neural network with time delays"Journal of Biological Systems. 8. 177-193 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] R.Ogita,H.Matsunage,T.Hara: "Asymptotic stability condition for a class of linear delay difference equations of higher order"J.Math.Anal.Appl.. 248. 83-96 (2000)

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      2000 Annual Research Report
  • [Publications] S.Sakata and T.Hara: "Dynamics of a linear differential system with piecewise constant argument"Dynam.Contin.Discrete Impuls.Systems. 7. 585-594 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 新井仁之: "フーリエ解析と関数解析学"培風館(近刊).

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Aikawa: "Boundary Harnack principle and Martin boundary for a uniform domain"Institut MIttag-Leffler,Report. 2. (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] H.Aikawa: "Integrability of superharmonic functions in a John domain"Proc.Amer.Math.Soc.. 128. 195-201 (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] H.Aikawa: "Evaluation of superharmonic functions using limits along lines"Bull.London Math.Soc.. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] H.Aikawa: "Boundary Harnack principle and Martin boundary for a uniform domain"J.Math.Soc.Japan. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] H.Arai: "Bergman-Carleson measueres and Bloch functions on strongly pseudoconvex domains"Reproducing Kernels and Their Applications(Kluwer Acad.Publ.). 21-31 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] H.Arai: "Singular elliptic operators related to harmonic analysis and complex analysis of several variables"Trends in Probablity and Related Analysis(World Sci.Publ.). 1-34 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] H.Arai: "Hardy spaces,Carleson measures and a gradient estimate for harmonic functions on negatively curved manifolds"Adv.Studies in Pure Math.. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] Y.Mizuta: "Boundary limits of spherical means for BLD abd monotone BLD functions in the unit ball"Acad.Sci.Fenn.Ser.A.I.Math.. 26. 45-60 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Y.Mizuta: "Growth properties of spherical means for monotone BLD functions in the unit ball"Acad.Sci.Fenn.Ser.A.I.Math.. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] Y.Mizuta: "Multiple exponential integrability for Risez potentials of functions in Orlicz classes"Advances in Math.Sci.and Applications. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] B.Gustafsson: "On potential theoretic skeletons of polyhedra"Geometricae Dedicata. 76. 1-30 (1999)

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      1999 Annual Research Report
  • [Publications] M.Sakai: "Linear combinations of harmonic measures and quadrature domains of signed measures with small supports"Proc.Edinburgh Math.Soc.. 42. 433-444 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 生源寺亨浩: "Hardy's inequality on finite networks"Mem.Fac.Sci.Shimane Univ.Ser.B:Mathematical Science. 32. 75-84 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 村上温: "Discrete Kuramochi function"Proc.3rd.Intern.Conference on Difference Equation and Applications. 313-322 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] W.Oettli: "Duality theorems on an infinite network"Optimization. (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] 山崎稀嗣: "Inequalities on networks"RIMS Kokyuroku. 1114. 184-193 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 村上温: "Inequalities on infinite networks"Mem.Fac.Sci.Shimane Univ.Ser.B:Mathematical Science. 33(to appear). (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] 陳小君: "Verification for existance of solutions of linear complementarity problems"Linear Algebra and Its Applications. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] M.Fukushima: "Large deviations and LIL's for Brownian motions on nested fractals"Osaka J.Math.. 36. 497-537 (1999)

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      1999 Annual Research Report
  • [Publications] M.Fukushima: "On limit theorems for Brownian motions on unbounded fractal sets"Fractal Geometry and Stochastics II'eds.Bandt,Graf,Zahle,Birkhauser. 227-237 (2000)

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      1999 Annual Research Report
  • [Publications] M.Fukushima: "On semimartingale characterizations of functionals of symmetric Markov processes"Electronic J.Probability. 4 Paper 18. 1-32 (1999)

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      1999 Annual Research Report
  • [Publications] Y.Gotoh: "A condition of quasiconformal extendability"Proc.Japan Acad.Ser.A Math.Sci.. 75. 58-60 (1999)

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      1999 Annual Research Report
  • [Publications] H.Sato: "One-parameter families of extreme descrete groups for Jorgensen's infequality"Contemporary Math.. (to appear).

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      1999 Annual Research Report
  • [Publications] H.Sato: "One-parameter families of extreme descrete groups"RIMS Kokyuuroku. 1104. 18-24 (1999)

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      1999 Annual Research Report
  • [Publications] E.Yanagida: "Recent topics on nonlinear partial differential equations-Structure of radial solutions for semilinear elliptic equations-(In Japanese)"Sugaku. 51. 276-290 (1999)

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      1999 Annual Research Report
  • [Publications] 森下博: "代用電荷によるポアソン方程式の数値計算法の改良"情報処理学会論文誌. 40. 3337-3344 (1999)

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      1999 Annual Research Report
  • [Publications] J.Sugie: "Global asymptotic stability of a predator-prey system of Holling type"Nonlinear Analysis. 38. 105-121 (1999)

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      1999 Annual Research Report
  • [Publications] Jitsuro Sugie: "Uniqueness of limit cycles in a predot prey system with Holling-type functional response"Quarterly of Applied Mathematics. (to appear).

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      1999 Annual Research Report
  • [Publications] 相川弘明(編集): "ポテンシャル論とその関連分野(数理解析研究所講究録1116)"京都大学数理解析研究所. (1999)

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      1999 Annual Research Report
  • [Publications] 新井仁之: "フーリエ解析と関数解析学(近刊)"培風館.

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      1999 Annual Research Report
  • [Publications] 水田義弘: "実解析入門-測度・積分・ソボレフ空間"倍風館. (1999)

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      1999 Annual Research Report
  • [Publications] S.Morosawa: "Holomorphic Dynamics"Cambridge Univ.Press. (1999)

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      1999 Annual Research Report

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Published: 1999-04-01   Modified: 2016-04-21  

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