INTEGRAL CONDITIONS FOR NONUNIFORM μ-DICHOTOMY ON THE HALF-LINE

被引：9

作者：

Bento, Antonio J. G. ^{[1
]}

Lupa, Nicolae ^{[2
]}

Megan, Mihail ^{[3
]}

Silva, Cesar M. ^{[1
]}

机构：

[1] Univ Beira Interior, Dept Matemat, P-6201001 Covilha, Portugal

[2] Politehn Univ Timisoara, Dept Math, Victoriei Sq 2, Timisoara 300006, Romania

[3] Acad Romanian Scientists, Independentei 54, Bucharest 050094, Romania

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2017年 / 22卷 / 08期

关键词：

Evolution operators; nonuniform dichotomies; Datko theorem; FUNCTIONAL-DIFFERENTIAL EQUATIONS; EXPONENTIAL DICHOTOMY; STABILITY QUESTION; LYAPUNOV FUNCTIONS;

D O I：

10.3934/dcdsb.2017163

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give necessary integral conditions and sufficient ones for the existence of a general concept of mu-dichotomy for evolution operators defined on the half-line which includes as particular cases the well-known concepts of nonuniform exponential dichotomy and nonuniform polynomial dichotomy, and also contains new situations. Additionally, we consider an adapted notion of Lyapunov function and use our results to obtain necessary and sufficient conditions for the existence of nonuniform mu-dichotomies using these Lyapunov functions.

引用

页码：3063 / 3077

页数：15

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