Study of the solution semigroup for integral equations and related topics

积分方程解半群的研究及相关课题

• 批准号: 22540211
• 负责人: MURAKAMI Satoru
• 金额: $ 1.58万
• 依托单位: Okayama University of Science
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540211/
• 关键词: 積分方程式; 解半群; スペクトル; 定数変化法の公式; 安定性; 中心多様体; 中心方程式; 相空間; 線形化原理; 特性方程式; 漸近挙動; ボルテラ方程式

We studied some qualitative properties of solutions in integral equations. Indeed, for linear integral equations we analyzed some spectral properties for the generator of the associated solution semigroup, and obtained an estimate on the essential spectral radius of the generator. Furthermore, we established a representation formula in the phase space for solutions of nonhomogeneous linear equations. Applying these results, we obtained Massera type results on the existence of bounded solutions, periodic solutions and so on. Also, for nonlinear integral equations we established the principle of linearization which is effectively applicable to stability problems in nonlinear equations.

研究了积分方程解的一些定性性质。对于线性积分方程，我们分析了伴随解半群的生成元的谱性质，得到了生成元的本质谱半径的估计。在此基础上，建立了非齐次线性方程组解在相空间中的表示公式。应用这些结果，我们得到了关于有界解、周期解等的Massera型结果，并对非线性积分方程建立了线性化原理，该原理可有效地应用于非线性方程的稳定性问题。

项目成果

Decomposition and Variation-of-Constants Formula in the Phase Space for Integral Equations

• DOI: 10.1619/fesi.55.479
• 发表时间: 2012
• 作者: H. Matsunaga;S. Murakami;V. M. Nguyen

On the uniqueness of positive solutions for two-point boundary value problems of Emden-Fower differ-ential equations

论Emden-Fower微分方程两点边值问题正解的唯一性

• 发表时间: 2010
• 期刊: Mathematica Bohemica
• 影响因子: 0.5
• 作者: H. Hamada;T. Honda and G. Kohr;A.Kubo;T. Kobayashi;S. Tanaka
• 通讯作者: S. Tanaka

Stability properties and almost periodic solutions of abstract functional differential equations with infinite delay

无限时滞抽象泛函微分方程的稳定性性质及近似周期解

• 发表时间: 2011
• 期刊: Libertys Mathematica
• 作者: E. Umezawa;et. Al.;Y. Hamaya
• 通讯作者: Y. Hamaya

Notes on complex hyperbolic triangle groups

关于复杂双曲三角形群的注释

• 发表时间: 2010
• 期刊: Conformal Geom. Dyn.
• 作者: S.Kamiya;J.R.Parker and J. Thompson
• 通讯作者: J.R.Parker and J. Thompson

Stability and instability linearization for integral equations

积分方程的稳定性和不稳定性线性化

• 发表时间: 2012
• 期刊: RIMS Kokyuroku
• 作者: T. Aoki;N. Honda;Y. Umeta;Kazunaga Tanaka;Hideaki Matsunaga
• 通讯作者: Hideaki Matsunaga