2000 Fiscal Year Annual Research Report

関数方程式の解の定性的研究とその応用

Research Project

Project/Area Number	10440047
Research Institution	SHIMANE UNIVERSITY
Principal Investigator	古用哲夫島根大学, 総合理工学部, 教授 (40039128)
Co-Investigator(Kenkyū-buntansha)	内藤敏機電気通信大学, 電気通信学部, 教授 (60004446) 上之郷高志東北学院大学, 教養学部, 教授 (60124567) 日野義之千葉大学, 理学部, 教授 (70004405) 村上悟岡山理科大学, 理学部, 教授 (40123963) 杉江実郎島根大学, 総合理工学部, 教授 (40196720)
Keywords	不動点定理 / 安定性 / 有界性 / 解曲線族 / 概周期解 / スペクトル / 振動性 / 抽象的関数微分方程式
Research Abstract	研究代表者の古用は、縮小写像による不動点定理が、微分方程式の安定性や有界性に有効であることを示すと共に、応用例を与えた。次に、零解が非一様に漸近安定であるような線形微分方程式系に対する非線形摂動を考え、シャウダーの不動点定理を用いて摂動系が漸近安定であるための十分条件を求めた。又、クラスノセルスキーの不動点定理を用いて、非線形微分方程式の零解の漸近安定性を証明すると共に、応用例を与えた。最後に、抽象的関数微分方程式が、外力項の関数のスペクトルと同じ構造をもつ概周期解をもつための必要十分条件について、有界関数のスペクトルの概念を用いて調べた。次に、研究分担者の日野義之教授(千葉大学)は、ヴォルテラ型微分方程式に対応する安定性と従来型安定性の同値性に関する成果を得た。同じく、研究分担者の上之郷高志教授(東北学院大学)は、関数方程式の解曲線族の構造に関する成果を得た。又、研究分担者の内藤敏機教授(電気通信大学)は、発展方程式の概周期解の存在に関してスペクトルを用いた新しい判定条件を開発した。更に、研究分担者の杉江実郎教授(島根大学)は、減衰係数をもつ2階非線形微分方程式の解の非振動性に関する成果を得た。次に、開極限軌道をもつリエナール方程式の解のダイナミクスを解明した。最後に、オイラー型の2階非線形微分方程式の解の振動性に関する判定法を開発した。最後に、研究分担者の村上悟教授(岡山理科大学)は、抽象的関数微分方程式に対する定数変化法に関する成果を得た。以上の諸研究に加えて、カタニア(イタリア)で開催された国際研究集会に招待され得られた成果を口答発表すると共に、この方面の世界的研究者であるアメリカ合衆国のバートン教授を招聘し、研究レビューを受けた。

Research Products
(22 results)

All Other

All Publications (22 results)

[Publications] T.A.Burton: "Periodic and asymptotically periodic solutions of neutral integral equations"Electronic Journal of Qualitaive Theory of Differential Equations. 10. 1-22 (2000)
[Publications] T.A.Burton: "Existence theorems and periodic solutions of neutral integral equations"Nonlinear Analysis. (発表予定).
[Publications] T.A.Burton: "Fixed points and problems in stability theory for ordinary and functional differential equations"Dynamic Systems and Applications. (発表予定).
[Publications] T.A.Burton: "A note on stability by Schauder's theorem"Funkcialaj Ekvacioj. (発表予定).
[Publications] T.A.Burton: "Krasnoselskii's fixed point theorem and stability"Nonlinear Analysis. (発表予定).
[Publications] Tetsuo Furumochi: "Boundedness and almost periodicity of solutions of partial functional differential equations"Journal of Differential Equations. (発表予定).
[Publications] Yoshiyuki Hino: "Total stability in abstract functional differential equations with infinite delay"Electronic Journal of Qualitative Theory of Differential Equations. 13. 1-9 (2000)
[Publications] Yoshiyuki Hino: "A variation-of-constants formula for abstract functional differential equations in the phase space"Journal of Differential Equations. (発表予定).
[Publications] Yoshiyuki Hino: "Limiting equations and some stability properties for asymptotically almost periodic functional differential equations with infinite delay"Tohoku Mathematical Journal. (発表予定).
[Publications] Yoshiyuki Hino: "Quasi-processes and stabilities in functional differential equations"Nonlinear Analysis. (発表予定).
[Publications] Takashi Kaminogo: "Kneser families in infinite-dimensional spaces"Nonlinear Analysis. (発表予定).
[Publications] Toshiki Naito: "A decomposition theorem and the existence of periodic solutions of periodic differential equations"Journal of Differential Equations. 160. 263-282 (2000)
[Publications] Toshiki Naito: "On the spectrum of some functional differential equations"Progress in Nonlinear Differential Equations and Their Applications. 42. 222-228 (2000)
[Publications] Jong Son Shin: "On stability of solutions in linear autonomous functional differential equations"Funkcialaj Ekvacioj. 43. 323-337 (2000)
[Publications] Toshiki Naito: "New spectral criteria for almost periodic solutions of evolution equations"Studia Mathematica. 発表予定.
[Publications] Jitsuro Sugie: "Oscillation of the Riemann-Weber version of Euler differential equations with delay"Georgian Mathematical Journal. 7. 577-584 (2000)
[Publications] Jitsuro Sugie: "Uniqueness of limit cycles in a predator-prey system of Holling type functional response"Quarterly of Apllied Mathematics. 58. 577-590 (2000)
[Publications] Jitsuro Sugie: "Oscillation criteria for second order nonlinear differential equations of Euler type"J.Math.Anal.Appl.. 253. 414-439 (2001)
[Publications] Jitsuro Sugie: "Lienard dynamics with an open orbit"Nonlinear Differential Equations Appl.. (発表予定).
[Publications] Jitsuro Sugie: "A nonoscillation theorem for second order nonlinear differential equations with decaying coefficients"J.Bull.London Math.Soc.. (発表予定).
[Publications] Satoru Murakami: "Spectral analysis of an operator associated with linear functional differential equations and its applications"Electronic Journal of Qualitative Theory of Differential Equations. 20. 1-15 (2000)
[Publications] Satoru Murakami: "Evolution semigroups and sums of commuting operators : a new approach to the admissibility theory of function spaces"Journal of Differential Equations. 164. 240-285 (2000)

2000 Fiscal Year Annual Research Report

関数方程式の解の定性的研究とその応用

Principal Investigator

古用 哲夫 島根大学, 総合理工学部, 教授 (40039128)

Research Products

[Publications] T.A.Burton: "Periodic and asymptotically periodic solutions of neutral integral equations"Electronic Journal of Qualitaive Theory of Differential Equations. 10. 1-22 (2000)

[Publications] T.A.Burton: "Existence theorems and periodic solutions of neutral integral equations"Nonlinear Analysis. (発表予定).

[Publications] T.A.Burton: "Fixed points and problems in stability theory for ordinary and functional differential equations"Dynamic Systems and Applications. (発表予定).

[Publications] T.A.Burton: "A note on stability by Schauder's theorem"Funkcialaj Ekvacioj. (発表予定).

[Publications] T.A.Burton: "Krasnoselskii's fixed point theorem and stability"Nonlinear Analysis. (発表予定).

[Publications] Tetsuo Furumochi: "Boundedness and almost periodicity of solutions of partial functional differential equations"Journal of Differential Equations. (発表予定).

[Publications] Yoshiyuki Hino: "Total stability in abstract functional differential equations with infinite delay"Electronic Journal of Qualitative Theory of Differential Equations. 13. 1-9 (2000)

[Publications] Yoshiyuki Hino: "A variation-of-constants formula for abstract functional differential equations in the phase space"Journal of Differential Equations. (発表予定).

[Publications] Yoshiyuki Hino: "Limiting equations and some stability properties for asymptotically almost periodic functional differential equations with infinite delay"Tohoku Mathematical Journal. (発表予定).

[Publications] Yoshiyuki Hino: "Quasi-processes and stabilities in functional differential equations"Nonlinear Analysis. (発表予定).

[Publications] Takashi Kaminogo: "Kneser families in infinite-dimensional spaces"Nonlinear Analysis. (発表予定).

[Publications] Toshiki Naito: "A decomposition theorem and the existence of periodic solutions of periodic differential equations"Journal of Differential Equations. 160. 263-282 (2000)

[Publications] Toshiki Naito: "On the spectrum of some functional differential equations"Progress in Nonlinear Differential Equations and Their Applications. 42. 222-228 (2000)

[Publications] Jong Son Shin: "On stability of solutions in linear autonomous functional differential equations"Funkcialaj Ekvacioj. 43. 323-337 (2000)

[Publications] Toshiki Naito: "New spectral criteria for almost periodic solutions of evolution equations"Studia Mathematica. 発表予定.

[Publications] Jitsuro Sugie: "Oscillation of the Riemann-Weber version of Euler differential equations with delay"Georgian Mathematical Journal. 7. 577-584 (2000)

[Publications] Jitsuro Sugie: "Uniqueness of limit cycles in a predator-prey system of Holling type functional response"Quarterly of Apllied Mathematics. 58. 577-590 (2000)

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

[Publications] Jitsuro Sugie: "Lienard dynamics with an open orbit"Nonlinear Differential Equations Appl.. (発表予定).

[Publications] Jitsuro Sugie: "A nonoscillation theorem for second order nonlinear differential equations with decaying coefficients"J.Bull.London Math.Soc.. (発表予定).

[Publications] Satoru Murakami: "Spectral analysis of an operator associated with linear functional differential equations and its applications"Electronic Journal of Qualitative Theory of Differential Equations. 20. 1-15 (2000)

[Publications] Satoru Murakami: "Evolution semigroups and sums of commuting operators : a new approach to the admissibility theory of function spaces"Journal of Differential Equations. 164. 240-285 (2000)

古用哲夫島根大学, 総合理工学部, 教授 (40039128)