Exponential dichotomies of evolution operators in Banach spaces

被引：24

作者：

Lupa, Nicolae ^{[1
]}

Megan, Mihail ^{[1
]}

机构：

[1] West Univ Timisoara, Fac Econ & Business Adm, Timisoara 300115, Romania

来源：

MONATSHEFTE FUR MATHEMATIK | 2014年 / 174卷 / 02期

关键词：

Evolution operator; Exponential dichotomy; Lyapunov function; HALF-LINE; DIFFERENTIAL-EQUATIONS; LYAPUNOV FUNCTIONALS; STABILITY; ADMISSIBILITY; EXPANSIVENESS; ROBUSTNESS; ROUGHNESS;

D O I：

10.1007/s00605-013-0517-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper considers three dichotomy concepts (exponential dichotomy, uniform exponential dichotomy and strong exponential dichotomy) in the general context of non-invertible evolution operators in Banach spaces. Connections between these concepts are illustrated. Using the notion of Green function, we give necessary conditions and sufficient ones for strong exponential dichotomy. Some illustrative examples are presented to prove that the converse of some implication type theorems are not valid.

引用

页码：265 / 284

页数：20

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