Behavior near hyperbolic stationary solutions for partial functional differential equations with infinite delay

被引：14

作者：

Adimy, Mostafa ^{[2
]}

Ezzinbi, Khalil ^{[1
]}

Ouhinou, Aziz ^{[1
]}

机构：

[1] Univ Cadi Ayyad, Fac Sci Semlalia, Dept Math, Marrakech, Morocco

[2] Univ Pau & Pays Adour, CNRS, Lab Math Appl, UMR 5142, F-64000 Pau, France

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2008年 / 68卷 / 08期

关键词：

semigroup; Hille-Yosida condition; integral solution; variation of constants formula; hyperbolic stationary solution; stable and unstable manifolds;

D O I：

10.1016/j.na.2007.01.051

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this work is to investigate the asymptotic behavior of solutions near hyperbolic stationary solutions for partial functional differential equations with infinite delay. We suppose that the linear part satisfies the Hille-Yosida condition on a Banach space and it is not necessarily densely defined. Firstly, we establish a new variation of constants formula for the nonhomogeneous linear equations. Secondly, we use this formula and the spectral decomposition of the phase space to show the existence of stable and unstable manifolds. The estimations of solutions on these manifolds are obtained. For illustration, we propose to study the stability of stationary solutions for the Lotka-Volterra model with diffusion. (C) 2007 Elsevier Ltd. All rights reserved.

引用

页码：2280 / 2302

页数：23

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