2001 Fiscal Year Annual Research Report

ポテンシャル解析の横断的研究

Research Project

Project/Area Number	11304008
Research Institution	Shimane University
Principal Investigator	杉江実郎島根大学, 総合理工学部, 教授 (40196720)
Co-Investigator(Kenkyū-buntansha)	水田義弘広島大学, 総合化学部, 教授 (00093815) 相川弘明島根大学, 総合理工学部, 教授 (20137889) 山崎稀嗣島根大学, 総合理工学部, 教授 (70032935) 原惟行大阪府立大学, 工学部, 教授 (20029565) 村田實東京工業大学, 理学部, 教授 (50087079)
Keywords	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
Research Abstract	・Euler型2階非線形微分方程式や減衰係数を持つ2階非線形微分方程式に対する振動条件の研究.(杉江) ・境界上のHolder連続な関数のDirichlet解がHolder連続になる条件を研究した。(相川) ・多調和関数に対するLiouville型定理、Bocher型定理について研究した。ソボレフ関数の境界値の存在を調べた。(水田) ・負曲率多様体上の調和関数からなるHardy空間、Carleson測度、Greenポテンシャルに関する結果を得た。(新井) ・熱方程式の解の持つ平均値の性質による熱球と帯状領域の特徴付けとその一般化。調和関数の勾配の条件による調和拡張と一意性定理。(鈴木) ・ホワイトヘッドリンクのヨルゲンセン数を決定した。また、実3次元空間における放物型のヨルゲンセン群を決定した。(佐藤) ・整函数の新しい組み合わせ的表現を与え、構造有限な整函数の場合に解析的な性質がどのように復元できるかを明らかにした。(谷口) ・フラクタル上の対称な確率過程から決まるディリクレ形式の定義域が、多くの場合ベソフ空間と呼ばれる関数空間となることを証明した。(熊谷) ・2種類の時間遅れτとhをもつ線形微分方程式の(τ,h)漸近安定領域の決定。時間遅れをもつ数理生態系微分方程式および差分方程式の定性的研究。(原) ・2種類の時間遅れτとhをもつ線形微分方程式の(τ,h)漸近安定領域の決定。(坂田) ・時間遅れとインパルスをもつ微分方程式の大域的吸収性および時間遅れをもつ差分方程式の漸近挙動についての研究(松永)

Research Products

(46 results)

All Other

All Publications (46 results)

[Publications] J.Sugie, K.Kita: "Oscillation criteria for second order nonlinear differential equations of Euler type"J. Math. Anal. Appl.. 253. 414-439 (2001)
[Publications] J.Sugie: "Lienard dynamics with an open limit orbit"NoDEA Nonlinear Differential Equations Appl.. 8. 83-97 (2001)
[Publications] J.Sugie: "A nonoscillation theorem for second order nonlinear differential equations with decaying coefficients"Bull. London Math. Soc.. 33. 299-308 (2001)
[Publications] J.Sugie, N.Yamaoka, Y.Obata: "Nonoscillation theorems for a nonlinear self-adjoint differential equation"Nonlinear Anal.. 47. 4433-4444 (2001)
[Publications] J.Sugie, N.Yamaoka: "An infinite sequence of nonoscillation theorems for second order nonlinear differential equations of Euler type"Nonlinear Anal.. (to appear).
[Publications] J.Sugie, K.Kita, N.Yamaoka: "Oscillation constant of second order nonlinear seif-adjoint differential equations"Ann. Mat. Pura Appl.. (to appear).
[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).
[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)
[Publications] H.Aikawa: "Holder continuity of Dirichiet solution for a general domain"Bull. London Math. Soc.. (to appear).
[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)
[Publications] T.A.Burton, T.Furumochi: "A note on stability by Schauder's theorem"Funkcialaj Ekvacioj. 44. 73-82 (2001)
[Publications] T.Furumochi: "Periodic solutions of Volterra difference equations and attractivity"Nonlinear Analysis. 44. 4013-4024 (2001)
[Publications] T.Futamura, K.Kishi, Y.Mizuta: "A generalization of the Liouville theorem to polyharmonic functions"J. Math. Soc. Japan. 53. 113-118 (2001)
[Publications] T.Futamura, K.Kishi, Y.Mizuta: "A generalization of Bocher's theorem for polyharmonic functions"Hiroshima Math. J.. 31. 59-70 (2001)
[Publications] T.Futamura.Y.Mizuta: "Existence of functions in weighted Sobolev spaces"Nagoya Math. J.. 164. 75-88 (2001)
[Publications] Y.Mizuta: "Boundary limits of functions in weighted Lebesgue or Sobolev classes"Revue Roumaine Math. Pures Appl.. 46. 67-75 (2001)
[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)
[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)
[Publications] H.Sato: "Jorgensen's inequality for classical Schottky groups of real type, II"J. Math. Soc. Japan. 53. 791-811 (2001)
[Publications] H.Sato: "The Picard group, the Whitehead link and Jorgensen groups"Proc. of the third ISAAC Congress. (to appear).
[Publications] M.Taniguchi: "Non-trivial deformation of an entire function abz+e^<bz>+c"Taiwan J. math.. 5. 641-646 (2001)
[Publications] M.Taniguchi: "Explicit representation of structurally finite entire functions"Proc. Japan Acad.. 77. 68-70 (2001)
[Publications] H.Morishita, E.Yanagida, S.Yotsutani: "Structural change of solutions for a scalar curvature equation"Differential and Integral Equations. 14. 273-288 (2001)
[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)
[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)
[Publications] S.Yotsutani: "Canonical form related with radial solutions of semilinear elliptic equations and its applications"Taiwanese J. Math.. 5. 507-517 (2001)
[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)
[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)
[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)
[Publications] M.Murata: "Martin boundaries of elliptic skew products, semismall perturbations, and fundamental solutions of parabolic equations"J. Fnuc. Anal.. (to appear).
[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).
[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).
[Publications] Y.Hino, T.Naito, N.V.Minh, J.S.Shin: "Almost Periodic Solutions of Differential Equations in Banach Spaces"Taylor and Francis. (2002)
[Publications] Y.Hino, S.Murakami: "Quasi-processes and stabilities in functional differential equations"Nonlinear Analysis. 47. 4025-4036 (2001)
[Publications] T.Hara, S.Sakata: "Dynamics of a delay differential system with periodically oscillatory coefficients"Nonlinear Anal.. 47. 4399-4408 (2001)
[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)
[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)
[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)
[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).
[Publications] H.Matsunaga, T.Hara, S.Sakata: "Global attractivity for a nonlinear difference equation with variable delay"Comput. Math. Appl.. 41. 543-551 (2001)
[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)
[Publications] H.Matsunaga, R.Ogita, K.Murakami: "Asymptotic behavior of a system of higher order linear difference equations"Nonlinear Anal.. 47. 4667-4677 (2001)
[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)
[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)
[Publications] Y.Saito, T.Hara, W.Ma: "Harmless delays for permanence and impersistence of Lotka-Volterra discrete predator-prey system"Nonlinear Anal.. (to appear).
[Publications] 新井仁之: "フーリエ解析と関数解析学"培風館. 293 (2001)

2001 Fiscal Year Annual Research Report

ポテンシャル解析の横断的研究

Principal Investigator

杉江 実郎 島根大学, 総合理工学部, 教授 (40196720)

Research Products

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

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

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

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

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

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

[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).

[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)

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

[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)

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

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

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

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

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

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

[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)

[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)

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

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

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

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

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

[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)

[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)

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

[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)

[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)

[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)

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

[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).

[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).

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

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

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

[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)

[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)

[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)

[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).

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

[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)

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

[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)

[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)

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

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

杉江実郎島根大学, 総合理工学部, 教授 (40196720)

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