Existence of Almost periodic solutions for functional differential equation

泛函微分方程近似周期解的存在性

• 批准号: 14540152
• 负责人: HINO Yoshiyuki
• 金额: $ 2.11万
• 依托单位: Chiba University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540152/
• 关键词: functional differential equations; almost periodic solution; periodic solution; Bohr Spectrum; constant formula; 安定性; スペクトル

If we consider an evolution equations which is a generalization of partial differential equations with infinite delay, The phase space has two types, that is, one is a uniform fading memory space and the other is a fading memory space. In this report, we have the followings for the above equations :(i)Phase space and decompositions.(ii)Liapunov's method and existence theorems of almost periodic solutions.(iii)existence theorem for linear systems.(iv)existence of almost periodic solution for nonlinear systems.In particular, existence theorems of almost periodic solutions and almost automorphic solutions are shown by using the constant formula. These are generalizations of Massera Type theorems for periodic systems. And, Bohr spectrum of the solutions are inherited from that of perturbed terms.

如果我们考虑一个发展方程，它是无限时滞偏微分方程的推广，相空间有两种类型，一种是一致的渐消记忆空间，另一种是渐消记忆空间。在本报告中，我们对上述方程有以下内容：（i）相空间和分解。（ii）李雅普诺夫方法和概周期解的存在性定理。（3）线性系统的存在性定理。（iv）非线性系统概周期解的存在性，特别地，利用常数公式证明了概周期解和概自守解的存在性定理。这些是周期系统的Massera型定理的推广。并且，解的玻尔谱继承了微扰项的玻尔谱。

项目成果

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. 179. 336-355 (2002)

Y.Hino，S.Murakami，T.Naito，N.V.Minh：“相空间中抽象泛函微分方程的常数变分公式”J。

Y.Hino, S.Murakami: "Almost automorphic solutions for abstract FDE"J.Math.Anal.Appl.. 286. 741-752 (2003)

Y.Hino, S.Murakami：“抽象 FDE 的几乎自守解”J.Math.Anal.Appl.. 286. 741-752 (2003)

Y.Hino, S.Murakami, N.V.Minh: "Decomposition of variation of constants formula for abstract functional differential equations"Funkcialaj Ekvacioj. 45. 341-372 (2002)

Y.Hino、S.Murakami、N.V.Minh：“抽象泛函微分方程常数变分公式的分解”Funkcialaj Ekvacioj。

Y.Hino, S.Murakami: "Limiting equations and some stability properties for asymptotically almost periodic"Tohoku Math.J.. 54. 239-257 (2002)

Y.Hino, S.Murakami：“渐近几乎周期的极限方程和一些稳定性属性”Tohoku Math.J.. 54. 239-257 (2002)

Y.Hino, T.Naito, N.V.Minh, J.S.Shin: "Almost Periodic Solutions of Differential Equations"Taylor and Fisher. 247 (2002)

Y.Hino、T.Naito、N.V.Minh、J.S.Shin：“微分方程的几乎周期解”泰勒和费舍尔。