Study of stability properties for positive linear equations with delay and related topics

时滞正线性方程的稳定性研究及相关课题

• 批准号: 19540203
• 负责人: MURAKAMI Satoru
• 金额: $ 1.83万
• 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: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19540203/
• 关键词: 関数方程式; 関数微分方程式; 正の方程式; 安定性; 漸近挙動; ボルテラ差分方程式; 特性方程式; スポクトル; スペクトル; 積分微分方程式

We studied qualitative properties of solutions in functional differential equations, integrodifferential equations and Volterra difference equations which are typical ones of equations with delay. Applying the variation-of-constants formula in the phase space for functional differential equations, we obtained a result on the behavior of solutions for equations with a perturbation. Also, we established a result on the existence of several invariant manifolds for nonlinear functional differential equations. Furthermore, treating integrodifferential equations mainly, we investigated the positivity of equations, and obtained a criterion on stabilities for positive equations.

研究了典型时滞方程泛函微分方程、积分微分方程和Volterra差分方程解的定性性质。在泛函微分方程的相空间中应用常量变分公式，我们得到了具有摄动的方程解的行为结果。此外，我们还建立了非线性函数微分方程的几个不变流形存在性的结果。进一步，主要针对积分微分方程，研究了方程的正性，得到了正方程稳定性判据。

项目成果

Uniform asymptotic stability and robust stability for positive linear Volterra difference equations

正线性 Volterra 差分方程的一致渐近稳定性和鲁棒稳定性

• 发表时间: 2008
• 期刊: Advances in Difference Equations 2008
• 作者: 壁谷 善継;二宮 広和;Kazuyuki Matsui;松本 和一郎;Satoru Murakami
• 通讯作者: Satoru Murakami

Perron type theorems for functional differetial equations with infinite delay in a Banach space

Banach 空间中无限延迟泛函微分方程的 Perron 型定理

• 发表时间: 2008
• 期刊: Nonlinear Anal. Vol.69
• 作者: K. Matsui;H. Matsunaga;S. Murakami
• 通讯作者: S. Murakami

Characterization of linear integral equations with nonnegative kernels

具有非负核的线性积分方程的表征

• 发表时间: 2007
• 期刊: J. Math. Anal. Appl. Vol.335
• 作者: T. Naito;J.S. Shin;S. Murakami;P.H.A. Ngoc
• 通讯作者: P.H.A. Ngoc

Characterization of positive linear integro-differential systems

正线性积分微分系统的表征

• 发表时间: 2007
• 期刊: Integral Equations and Operator Theory Vol.58
• 作者: T. Naito;S. Murakami;J.S. Shin;P.H.A. Pham
• 通讯作者: P.H.A. Pham

Stability and robust stability of positive linear Volterra difference equations

• DOI: 10.1002/rnc.1335
• 发表时间: 2009-03
• 期刊: International Journal of Robust and Nonlinear Control
• 影响因子: 3.9
• 作者: P. H. A. Ngoc;Toshiki Naito;J. Shin;S. Murakami