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Approach to the qualitative theory of functional equations by phase plane analysis

Research Project

Project/Area Number 16540152
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

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

Co-Investigator(Kenkyū-buntansha) FURUMOCHI T.  Shimane Univ., Dept. of Math., Professor, 総合理工学部, 教授 (40039128)
MACHIHARA S.  Shimane Univ., Dept. of Math., Associate Professor, 総合理工学部, 助教授 (20346373)
MATSUNAGA H.  Osaka Pref. Univ., Dept. of Math., Lecture, 大学院・工学研究科, 講師 (40332960)
YAMAOKA N.  Sophia Univ., Dept. of Math., Assistant Professor, 理工学部, 助手 (90433789)
相川 弘明  北海道大学, 大学院・理学研究科, 教授 (20137889)
Project Period (FY) 2004 – 2006
Project Status Completed (Fiscal Year 2006)
Budget Amount *help
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2006: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2005: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2004: ¥1,600,000 (Direct Cost: ¥1,600,000)
Keywordsoscillation / phase plane analysis / Lienard system / limit cycle / homoclinic orbit / global asymptotic stability / p-Laplacian / half-linear differential equation / p・ラプラシアン / 被食者・捕食者モデル / Lienard方程式系 / 解の振動性 / 楕円型方程式 / p-Laplacian / 摂動項 / homoclinic軌道 / 自己随伴型非線形微分方程式 / 時間遅れをもつ差分方程式系
Research Abstract

(i) We considered a nonlinear delay difference equation, and gave sufficient conditions for all nontrivial solutions to be oscillatory and sufficient conditions for the existence of a nonoscillatory solution. Our results were proved by use of phase plane analysis for a system equivalent to this equation.
(ii) The prototype of Lienard system was first formulated by the French physicist A. Lienard in 1928. The system played an important role in the development of the qualitative theory of differential equations. In this research, we gave sufficient conditions for the zero solution of nonautonomous Lienard systems to be globally asymptotically stable. We also investigated the existence of homoclinic orbits in generalized Lienard systems and obtained some conditions under which the Lienard system has homoclinic orbits. As a practical application, we gave a necessary and sufficient condition for the the existence of homoclinic orbits in Gause-type predator-prey models which are under the inf … More luence of an Allee effect.
(iii) It is well-known that the solution space of linear differential equations has homogeneity and additivity; that is, any multiple of a solution is also a solution and the sum of two solutions is another solution. The investigation of half-linear differential equations has attracted considerable attention in the last two decades. The term half-linear differential equations is derived from the fact that the solution space has just one half of the above properties, namely, homogeneity (but not additivity). Half-linear differential equations are sometimes called differential equations with the one-dimensional p-Laplacian. In this research, we discussed the asymptotic behavior of solutions and the global asymptotical stability of the zero solution of nonautonomous half-linear differential systems.
(iv) We dealt with the oscillation problem for various differential equations such as self-adjoint differential equations, half-linear differential equations, nonlinear differential equations with p-Laplacian or with perturbed terms, and elliptic equations. We presented sufficient conditions for all nontrivial solutions to be oscillatory and sufficient conditions for all nontrivial solutions to be nonoscillatory. The obtained theorems extended many previous results on this problem. Our main method is phase plane analysis for a system equivalent to each equation.
(v) Combining Lienard system and differential equations with the one-dimensional p-Laplacian, we considered Lienard-type system with p-Laplacian. We gave sufficient conditions under which this new system has at least one stable limit cycle. The main results were proved by means of phase plane analysis with the Poincare-Bendixson theorem. Less

Report

(4 results)
  • 2006 Annual Research Report   Final Research Report Summary
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • Research Products

    (115 results)

All 2007 2006 2005 2004 Other

All Journal Article (115 results)

  • [Journal Article] Exact stability criteria for delay differential and difference equations2007

    • Author(s)
      H.Matsunaga
    • Journal Title

      Applied of Mathematics Letters Vol.20, No.2

      Pages: 183-188

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Oscillation criteria for second order damped nonlinear differential equations with p-Laplacian2007

    • Author(s)
      N.Yamaoka
    • Journal Title

      Journal of Mathematical Analysis and Applications Vol.325, No.2

      Pages: 932-948

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Exact stability criteria for delay differential and difference equations2007

    • Author(s)
      H.Matsunaga
    • Journal Title

      Appl. Math. Lett. 20

      Pages: 183-188

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Oscillation criteria for second order damped nonlinear differential equations with p-Laplacian2007

    • Author(s)
      N.Yamaoka
    • Journal Title

      J. Math. Anal. Appl. 325

      Pages: 932-948

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Comparison theorems for oscillation of second-order half-linear differential equations2006

    • Author(s)
      J.Sugie, N.Yamaoka
    • Journal Title

      Acta Mathematica Hungarica Vol. 111, No.1-2

      Pages: 165-179

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A nonoscillation theorem for nonlinear differential equations with p-Laplacian2006

    • Author(s)
      J.Sugie, M.Onitsuka
    • Journal Title

      Proceedings of the Royal Society of Edinburgh. Section A Vol.136, No.3

      Pages: 633-647

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Homoclinic orbits in predator-prey systems with a non-smooth prey growth rate2006

    • Author(s)
      J.Sugie, K.Kimoto
    • Journal Title

      Quarterly of Applied Mathematics Vol.64, No.3

      Pages: 447-461

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Multilayer structures of second-order linear differential equations of Euler type and their application to nonlinear oscillations2006

    • Author(s)
      N.Yamaoka, J.Sugie
    • Journal Title

      Ukrains'kyi Matematychnyi Zhurnal Vol.58, No.12

      Pages: 1704-1714

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Existence theorems and periodic solutions of neutral difference equations2006

    • Author(s)
      T.Furumochi, T.Tsuchie, H.Wada
    • Journal Title

      Cubo Mathematical Journal Vol.8, No.3

      Pages: 35-46

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Liapunov functions and boundedness in difference equations2006

    • Author(s)
      T.Furumochi, K.Hishitani, K.Tsuchihashi
    • Journal Title

      Dynamics of Continuous, Discrete and Impulsive Systems Proceedings Vol.2

      Pages: 331-339

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Comparison theorems for oscillation of second-order half-linear differential equations2006

    • Author(s)
      J.Sugie, N.Yamaoka
    • Journal Title

      Acta Math. Hungar. 111

      Pages: 165-179

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A nonoscillation theorem for nonlinear differential equations with p-Laplacian2006

    • Author(s)
      J.Sugie, M.Onitsuka
    • Journal Title

      Proc. Roy. Soc. Edinburgh Sect. A 136

      Pages: 633-647

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Homoclinic orbits in predator-prey systems with a non-smooth prey growth rate2006

    • Author(s)
      J.Sugie, K.Kimoto
    • Journal Title

      Quart. Appl. Math. 64

      Pages: 447-461

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Multilayer structures of second-order linear differential equations of Euler type and their application to nonlinear oscillations2006

    • Author(s)
      N.Yamaoka, J.Sugie
    • Journal Title

      Ukrain. Mat. Zh. 58

      Pages: 1704-1714

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Asymptotic behavior of solutions of half-linear differential equations with variable coefficients2006

    • Author(s)
      J.Sugie, A.Yamaguchi, M.Onitsuka
    • Journal Title

      RIMS Kokyukoku 1474

      Pages: 84-101

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Oscillation problem for half-linear differential equations with periodic damping2006

    • Author(s)
      K.Matsumura, N.Yamaoka, J.Sugie
    • Journal Title

      RIMS Kokyukoku 1474

      Pages: 154-161

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Existence theorems and periodic solutions of neutral difference equations2006

    • Author(s)
      T.Furumochi, T.Tsuchie, H.Wada
    • Journal Title

      Cubo Math. J. 8

      Pages: 35-46

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Liapunov functions and boundedness in difference equations2006

    • Author(s)
      T.Furumochi, K.Hishitani, K.Tsuchihashi
    • Journal Title

      Dynam. Contin. Discrete Impuls. Systems Proceedings 2

      Pages: 331-339

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Multilayer structures of second-order linear differential equations of Euler type and their application to nonlinear oscillations2006

    • Author(s)
      N.Yamaoka, J.Sugie
    • Journal Title

      Ukrainian Math. J. 58

      Pages: 1704-1714

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A nonosciliation theorem for nonlinear differential equations with p-Laplacian2006

    • Author(s)
      J.Sugie, M.Onitsuka
    • Journal Title

      Proceedings of the Royd Society of Edinburgh. Section A Vol.136, No.3

      Pages: 633-647

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Homoclililc orbits in predator-prey systems with a non-smooth prey growth rate2006

    • Author(s)
      J.Sugie, K.Kimoto
    • Journal Title

      Quarterly of Applied Mathematics Vol.64, No.3

      Pages: 447-461

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Multilayer structures of second-order linear differential equations of Euler type and their application to nonlinear osciliations2006

    • Author(s)
      N.Yamaoka, J.Sugie
    • Journal Title

      Ukrains'kyi Matematychnyi Zhurnal Vol.58, No.12

      Pages: 1704-1714

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Comparison theorems for oscillation of second-order half linear differential equations2006

    • Author(s)
      J.Sugie, N.Yamaoka
    • Journal Title

      Acta Mathematica Hungarica Vol.111,No.1-2

      Pages: 165-179

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Growth conditions for oscillation of nonlinear differential equations with p-Laplacian2005

    • Author(s)
      J.Sugie, N.Yamaoka
    • Journal Title

      Journal of Mathematical Analysis and Applications Vol.306, No.1

      Pages: 18-34

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Oscillation caused by delay perturbation in half-linear differential equations2005

    • Author(s)
      N.Yamaoka, J.Sugie
    • Journal Title

      Dynamic Systems and Applications Vol.14, No.3-4

      Pages: 365-379

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Homoclinic orbits in generalized Lienard systems2005

    • Author(s)
      J.Sugie
    • Journal Title

      Journal of Mathematical Analysis and Applications Vol.309, No.1

      Pages: 211-226

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Stabilities in FDEs by Schauder's theorem2005

    • Author(s)
      T.Furumochi
    • Journal Title

      Nonlinear Analysis Vol.63, No.5-7

      Pages: 217-224

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Endpoint Strichartz estimates and global solutions for the nonlinear Dirac equation2005

    • Author(s)
      S.Machihara, M.Nakamura, K.Nakanishi, T.Ozawa
    • Journal Title

      Journal of Functional Analysis Vol.219, No.2

      Pages: 1-20

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] One dimensional Dirac equation with quadratic nonlinearities2005

    • Author(s)
      S.Machihara
    • Journal Title

      Discrete and Continuous Dynamical Systems Vol.13, No.1-2

      Pages: 277-290

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A note on asymptotic stability of delay difference systems2005

    • Author(s)
      H.Matsunaga
    • Journal Title

      Journal of Inequality and Applications. Vol.2005, No.2

      Pages: 119-125

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Asymptotic behavior of solutions of functional difference equations2005

    • Author(s)
      H.Matsunaga, S.Murakami
    • Journal Title

      Journal of Mathematical Analysis and Applications Vol.305, No.2

      Pages: 391-410

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Oscillation and nonoscillation theorems for second order nonlinear differential equations with p-Laplacian2005

    • Author(s)
      N.Yamaoka
    • Journal Title

      Mem. Fac. Sci. Eng. Shimane Univ. Ser. B Math. Sci. Vol.38

      Pages: 17-30

    • NAID

      110006939928

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Growth conditions for oscillation of nonlinear differential equations with p-Laplacian2005

    • Author(s)
      J.Sugie, N.Yamaoka
    • Journal Title

      J. Math. Anal. Appl. 306

      Pages: 18-34

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Homoclinic orbits in generalized Lienard systems2005

    • Author(s)
      J.Sugie
    • Journal Title

      J. Math. Anal. Appl. 309

      Pages: 211-226

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Oscillation caused by delay perturbation in half-linear differential equations2005

    • Author(s)
      N.Yamaoka, J.Sugie
    • Journal Title

      Dynam. Systems Appl. 14

      Pages: 365-379

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Global phase portraits of planar autonomous half-linear systems2005

    • Author(s)
      M.Onitsuka, A.Yamaguchi, J.Sugie
    • Journal Title

      RIMS Kokyukoku 1445

      Pages: 88-98

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Oscillation and comparison theorems for second-order half-linear differential equations2005

    • Author(s)
      N.Yamaoka, J.Sugie
    • Journal Title

      RIMS Kokyukoku 1445

      Pages: 110-120

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Asymptotic behavior of nonlinear functional differential equations by Schauder's theorem2005

    • Author(s)
      T.A.Burton, T.Furumochi
    • Journal Title

      Nonlinear Stud. 12

      Pages: 73-84

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Stabilities in FDEs by Schauder's theorem2005

    • Author(s)
      T.Furumochi
    • Journal Title

      Nonlinear Anal. 63

      Pages: 217-224

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Endpoint Strichartz estimates and global solutions for the nonlinear Dirac equation2005

    • Author(s)
      S.Machihara, M.Nakamura, K.Nakanishi, T.Ozawa
    • Journal Title

      J. Funct. Anal. 219

      Pages: 1-20

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] One dimensional Dirac equation with quadratic nonlinearities2005

    • Author(s)
      S.Machihara
    • Journal Title

      Discrete Contin. Dynam. Systems 13

      Pages: 277-290

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A note on asymptotic stability of delay difference systems2005

    • Author(s)
      H.Matsunaga
    • Journal Title

      J. Inequal. Appl. 2005

      Pages: 119-125

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Asymptotic behavior of solutions of functional difference equations2005

    • Author(s)
      H.Matsunaga, S.Murakami
    • Journal Title

      J. Math. Anal. Appl. 305

      Pages: 391-410

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Oscillation and nonoscillation theorems for second order nonlinear differential equations with p-Laplacian2005

    • Author(s)
      N.Yamaoka
    • Journal Title

      Mem. Fac. Sci. Eng. Shimane Univ. Ser. B Math. Sci. 38

      Pages: 17-30

    • NAID

      110006939928

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Growth conditions for oscillation of nonlinear differential equations with p-Laplacian2005

    • Author(s)
      J.Sugie, N.Yamaoka
    • Journal Title

      Journal of Mathematical Analysis and Applications Vol.306,No.1

      Pages: 18-34

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Homoclinic orbits in generalized Lienard systems2005

    • Author(s)
      J.Sugie
    • Journal Title

      Journal of Mathematical Analysis and Applications Vol.309,No.1

      Pages: 211-226

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Oscillation caused by delay perturbation in half-linear differential equations2005

    • Author(s)
      N.Yamaoka, J.Sugie
    • Journal Title

      Dynamic Systems and Applications Vol.14,No.3-4

      Pages: 365-379

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Endpoint Strichartz estimates and global solutions for the nonlinear Dirac equation2005

    • Author(s)
      S.Machihara, M.Nakamura, K.Nakanishi, T.Ozawa
    • Journal Title

      Journal of Functional Analysis Vol.219,No.1

      Pages: 1-20

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Phase plane analysis in oscillation theory of nonlinear delay differential equations2004

    • Author(s)
      J.Sugie, Y.Ono
    • Journal Title

      Journal of Difference Equations and Applications Vol.10, No.1

      Pages: 99-116

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Global asymptotic stability of non-autonomous systems of Lienard type2004

    • Author(s)
      J.Sugie, Y.Amano
    • Journal Title

      Journal of Mathematical Analysis and Applications Vol.289, No.2

      Pages: 673-690

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Oscillation of solutions of second-order nonlinear self adjoint differential equations2004

    • Author(s)
      J.Sugie, N.Yamaoka
    • Journal Title

      Journal of Mathematical Analysis and Applications Vol.291, No.2

      Pages: 387-405

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Influence of nonlinear perturbed terms on the oscillation of elliptic equations2004

    • Author(s)
      N.Yamaoka, J.Sugie
    • Journal Title

      Proceedings of the American Mathematical Society Vol.132, No.8

      Pages: 2281-2290

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Oscillation criteria of Kneser-Hille type for second-order differential equations with nonlinear perturbed terms2004

    • Author(s)
      J.Sugie
    • Journal Title

      Rocky Mountain Journal of Mathematics Vol.34, No.4

      Pages: 1519-1537

    • NAID

      120006221256

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Stabilities in Volterra difference equations on a Banach space2004

    • Author(s)
      T.Furumochi, S.Murakami, Y.Nagabuchi
    • Journal Title

      Fields Institute Communications Vol.42

      Pages: 159-176

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary 2004 Annual Research Report
  • [Journal Article] Asymptotic behavior of some functional differential equations by Schauder's theorem2004

    • Author(s)
      T.Furumochi
    • Journal Title

      Proc. 7th Coll. Qual. Theory Differ. Equ. No.10

      Pages: 1-11

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Volterra difference equations on a Banach space and abstract differential equations with piecewise continuous delays2004

    • Author(s)
      T.Furumochi, S.Murakami, Y.Nagabuchi
    • Journal Title

      Japanese Journal of Mathematics Vol.30, No.2

      Pages: 387-412

    • NAID

      10014334745

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A generalization of Wiener's lemma and its application to Volterra difference equations on a Banach space2004

    • Author(s)
      T.Furumochi, S.Murakami, Y.Nagabuchi
    • Journal Title

      Journal of Difference Equations and Applications. Vol.10, No.13-15

      Pages: 1201-1214

    • NAID

      120005587462

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Asymptotic behavior of nonlinear functional differential equations by Schauder's theorem2004

    • Author(s)
      T.A.Burton, T.Furumochi
    • Journal Title

      Nonlinear Studies Vol.12, No. l

      Pages: 73-84

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Small global solutions for nonlinear Dirac equations2004

    • Author(s)
      S.Machihara, M.Nakamura, T.Ozawa
    • Journal Title

      Differential Integral Equations Vol.17, No.5-6

      Pages: 623-636

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Stability regions for a class of delay difference systems2004

    • Author(s)
      H.Matsunaga
    • Journal Title

      Fields Institute Communications Vol.42

      Pages: 273-283

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Some invariant manifolds for functional difference equations with infinite delay2004

    • Author(s)
      H.Matsunaga, S.Murakami
    • Journal Title

      Journal of Difference Equations and Applications Vol.10, No.7

      Pages: 661-689

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Phase plane analysis in oscillation theory of nonlinear delay difference equations2004

    • Author(s)
      J.Sugie, Y.Ono
    • Journal Title

      J. Differ. Equations Appl. 10

      Pages: 99-116

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Global asymptotic stability of non-autonomous systems of Lienard type2004

    • Author(s)
      J.Sugie, Y.Amano
    • Journal Title

      J. Math. Anal. Appl. 289

      Pages: 673-690

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Oscillation of solutions of second-order nonlinear self-adjoint differential equations2004

    • Author(s)
      J.Sugie, N.Yamaoka
    • Journal Title

      J. Math. Anal. Appl. 291

      Pages: 387-405

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Influence of nonlinear perturbed terms on the oscillation of elliptic equations2004

    • Author(s)
      N.Yamaoka, J.Sugie
    • Journal Title

      Proc. Amer. Math. Soc. 132

      Pages: 2281-2290

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Oscillation criteria of Kneser-Hille type for second-order differential equations with nonlinear perturbed terms2004

    • Author(s)
      J.Sugie
    • Journal Title

      Rocky Mountain J. Math. 34

      Pages: 1519-1537

    • NAID

      120006221256

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Oscillation theorems for nonlinear differential equations with p-Laplacian and its application to elliptic equation2004

    • Author(s)
      N.Yamaoka, J.Sugie
    • Journal Title

      RIMS Kokyukoku 1372

      Pages: 151-158

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Stabilities in Volterra difference equations on a Banach space2004

    • Author(s)
      T.Furumochi, S.Murakami, Y.Nagabuchi
    • Journal Title

      Fields Institute Communications 42

      Pages: 159-175

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Asymptotic behavior of solutions of some functional differential equations by Schauder's theorem2004

    • Author(s)
      T.Furumochi
    • Journal Title

      Proc. 7th Coll. QTDE No.10

      Pages: 1-11

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Volterra difference equations on a Banach space and abstract differential equations with piecewise continuous delays2004

    • Author(s)
      T.Furumochi, S.Murakami, Y.Nagabuchi
    • Journal Title

      Japan. J. Math. 30

      Pages: 387-412

    • NAID

      10014334745

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A generalization of Wiener's lemma and its application to Volterra difference equations on a Banach space2004

    • Author(s)
      T.Furumochi, S.Murakami, Y.Nagabuchi
    • Journal Title

      J. Differ. Equations Appl. 10

      Pages: 1201-1214

    • NAID

      120005587462

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Small global solutions for nonlinear Dirac equations2004

    • Author(s)
      S.Machihara, M.Nakamura, T.Ozawa
    • Journal Title

      Differential Integral Equations 17

      Pages: 623-636

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Small global solutions for the nonlinear Dirac equation2004

    • Author(s)
      S.Machihara, M.Nakamura, T.Ozawa
    • Journal Title

      RIMS Kokyukoku 1388

      Pages: 81-87

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Stability regions for a class of delay difference systems2004

    • Author(s)
      H.Matsunaga
    • Journal Title

      Fields Institute Communications 42

      Pages: 273-283

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Some invariant manifolds for functional difference equations with infinite delay2004

    • Author(s)
      H.Matsunaga, S.Murakami
    • Journal Title

      J. Differ. Equations Appl. 10

      Pages: 661-689

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Phase plane analysis in oscillation theory of nonlinear delay differential equations2004

    • Author(s)
      J.Sugie, Y.Ono
    • Journal Title

      Journal of Difference Equations and Applications Vol.10,No.1

      Pages: 99-116

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Global asymptotic stability of non-autonomous systems of Lienard type2004

    • Author(s)
      J.Sugie, Y.Amano
    • Journal Title

      Journal of Mathematical Analysis and Applications Vol.289,No.2

      Pages: 673-690

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Oscillation of solutions of second-order nonlinear self-adjoint differential equations2004

    • Author(s)
      J.Sugie, N.Yamaoka
    • Journal Title

      Journal of Mathematical Analysis and Applications Vol.291,No.2

      Pages: 387-405

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Influence of nonlinear perturbed terms on the oscillation of elliptic equations2004

    • Author(s)
      N.Yamaoka, J.Sugie
    • Journal Title

      Proceedings of the American Mathematical Society Vol.132,No.8

      Pages: 2281-2290

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Oscillation criteria of Kneser-Hille type for second-order differential equations with nonlinear perturbed terms2004

    • Author(s)
      J.Sugie
    • Journal Title

      Rocky Mountain Journal of Mathematics Vol.34,No.4

      Pages: 1519-1537

    • NAID

      120006221256

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Fatou and Littlewood theorems for Poisson integrals with respect to non-integrable kernels2004

    • Author(s)
      H.Aikawa
    • Journal Title

      Complex Variables Theory and Application Vol.49,No.7-9

      Pages: 511-528

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Potential-theoretic characterizations of nonsmooth domains2004

    • Author(s)
      H.Aikawa
    • Journal Title

      The Bulletin of the London Mathematical Society Vol.36,No.4

      Pages: 469-482

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Volterra difference equations on a Banach space and abstract differential equations with piecewise continuous delays2004

    • Author(s)
      T.Furumochi, S.Murakami, Y.Nagabuchi
    • Journal Title

      Japanese Journal of Mathematics Vol.30,No.2

      Pages: 387-412

    • NAID

      10014334745

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A generalization of Wiener's lemma and its application to Volterra difference equations on a Banach space2004

    • Author(s)
      T.Furumochi, S.Murakami, Y.Nagabuchi
    • Journal Title

      Journal of Difference Equations and Applications Vol.10,No.13-15

      Pages: 1201-1214

    • NAID

      120005587462

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Small global solutions for nonlinear Dirac equations2004

    • Author(s)
      S.Machihara, M.Nakamura, T.Ozawa
    • Journal Title

      Differential Integral Equations Vol.17,No.5-6

      Pages: 623-636

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Stability regions for a class of delay differential equations2004

    • Author(s)
      H.Matsunaga
    • Journal Title

      Fields Institute Communications Vol.42

      Pages: 273-283

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Some invariant manifolds for functional difference equations with infinite delay2004

    • Author(s)
      H.Matsunaga, S.Murakami
    • Journal Title

      Journal of Difference Equations and Applications Vol.10,No.7

      Pages: 661-689

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Existence of limit cycles for Lienard-type systems with p-Laplacian

    • Author(s)
      J.Sugie, A.Kono, A.Yamaguchi
    • Journal Title

      NoDEA Nonlinear Differential Equations and Applications (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Asymptotic behavior of solutions of nonautonomous half-linear differential systems

    • Author(s)
      J.Sugie, M.Onitsuka, A.Yamaguchi
    • Journal Title

      Studia Scientiarum Mathematicarum Hungarica. (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Nonoscillation criteria for second-order nonlinear differential equations with decaying coefficients

    • Author(s)
      J.Sugie
    • Journal Title

      Mathematische Nachrichten (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Geometrical conditions for oscillation of second-order linear and half linear differential equations

    • Author(s)
      J.Sugie
    • Journal Title

      Acta Mathematica Hungarica (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] The limits of the solutions of a linear delay difference system

    • Author(s)
      H.Matsunaga
    • Journal Title

      Proceedings of the International Conference on Difference Equations (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Global attractivity for a nonlinear differential equation with unbounded delay

    • Author(s)
      H.Matsunaga
    • Journal Title

      Qual. Theory Differential Equations Appl. (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Existence of limit cycles for Lienard-type systems with p-Laplacian

    • Author(s)
      J.Sugie, A.Kono, A.Yamaguchi
    • Journal Title

      NoDEA Nonlinear Differential Equations Appl. (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Asymptotic behavior of solutions of nonautonomous half-linear differential systems,

    • Author(s)
      J.Sugie, M.Onitsuka, A.Yamaguchi
    • Journal Title

      Studia. Sci. Math. Hungar. (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Nonoscillation criteria for second-order nonlinear differential equations with decaying coefficients

    • Author(s)
      J.Sugie
    • Journal Title

      Math. Nachr. (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Geometrical conditions for oscillation of second-order linear and half-linear differential equations

    • Author(s)
      J.Sugie
    • Journal Title

      Acta Math. Hungar. (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Global asymptotic stability for half-linear differential equations with bounded coefficients

    • Author(s)
      M.Onitsuka, J.Sugie
    • Journal Title

      RIMS Kokyukoku (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] The limits of the solutions of a linear delay difference system, Proceedings of the International Conference on Difference Equations

    • Author(s)
      H.Matsunaga
    • Journal Title

      Special Functions and Applications (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Global attractivity for a nonlinear differential equation with unbounded delay

    • Author(s)
      H.Matsunaga
    • Journal Title

      Qual. Theory Differential Equations Appl. (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Exixtence of limit cycles for Lienard-type systems with p-Laplacian

    • Author(s)
      J.Sugie, A.Kono, A.Yamaguchi
    • Journal Title

      NoDEA Nonlinear Differential Equations and Applications 印刷中(印刷中)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Asymptotic behavior of solutions of nonautonomous half-linear differential systems

    • Author(s)
      J.Sugie, M.Onitsuka, A.Yamaguchi
    • Journal Title

      Studia Scientiarum Mathematicarum Hungarica. 印刷中(印刷中)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Nonosciliation criteria for second-order nonlinear differential equations with decaying coefficients

    • Author(s)
      J.Sugie
    • Journal Title

      Mathematische Nachrichten 印刷中(印刷中)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Geometrical conditions for oscillation of second-order linear and half-linear differential equations

    • Author(s)
      J.Sugie
    • Journal Title

      Acta Mathematica Hungarica 印刷中(印刷中)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Existence of limit cycles for Lienard-type systems with p-Laplacian

    • Author(s)
      J.Sugie, A.Kono, A.Yamaguchi
    • Journal Title

      NoDEA Nonlinear Differential Equations and Applications (印刷中)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A nonoscillation theorem for nonlinear differential equations with p-Laplacian

    • Author(s)
      J.Sugie, M.Onitsuka
    • Journal Title

      Proceedings of the Royal Society of Edinburgh. Section A (印刷中)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Homoclinic orbits in predator-prey systems with a non-smooth prey growth rate

    • Author(s)
      J.Sugie, K.Kimoto
    • Journal Title

      Quarterly of Applied Mathematics (印刷中)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Growth conditions for oscillation of nonlinear differential equations with p-Laplacian

    • Author(s)
      J.Sugie, N.Yamaoka
    • Journal Title

      Journal of Mathematical Analysis and Applications 印刷中

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Oscillation caused by delay perturbation in half-linear differential equations

    • Author(s)
      N.Yamaoka, J.Sugie
    • Journal Title

      Dynamic Systems and Applications 印刷中

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Homoclinic orbits in generalized Lienard systems

    • Author(s)
      J.Sugie
    • Journal Title

      Journal of Mathematical Analysis and Applications 印刷中

    • Related Report
      2004 Annual Research Report
  • [Journal Article] The 3G inequality for a uniformly John domain

    • Author(s)
      H.Aikawa, T.Lundh
    • Journal Title

      Kodai Mathematical Journal 印刷中

    • NAID

      130003574484

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Carleson type estimates for p-harmonic functions and the conformal Martin boundary of John domains in metric measure spaces

    • Author(s)
      H.Aikawa, N.Shanmugalingam
    • Journal Title

      The Michigan Mathematical Journal 印刷中

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Holder estimates of p-harmonic extension operators

    • Author(s)
      H.Aikawa, N.Shanmugalingam
    • Journal Title

      Journal of Differential Equations 印刷中

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A note on asymptotic stability of delay difference systems

    • Author(s)
      H.Matsunaga
    • Journal Title

      Journal of inequalities and Applications 印刷中

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Asymptotic behavior of solutions of functional difference equations

    • Author(s)
      H.Matsunaga, S.Murakami
    • Journal Title

      Journal of Mathematical Analysis and Applications 印刷中

    • Related Report
      2004 Annual Research Report

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Published: 2004-04-01   Modified: 2016-04-21  

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