DICHOTOMY AND ASYMPTOTIC EQUIVALENCE OF BOUNDED SOLUTIONS FOR SYSTEMS IN BANACH SPACES

被引：0

作者：

Bai, Yujie ^{[1
,2
]}

Huang, Haiyang ^{[1
]}

Zhou, Linfeng ^{[1
]}

机构：

[1] Sichuan Univ, Sch Math, Chengdu 610064, Sichuan, Peoples R China

[2] Taiyuan Inst Technol, Dept Sci, Taiyuan 030008, Shanxi, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2024年

关键词：

Dichotomy; asymptotic equivalence; bounded solution; Green function; infinite dimension;

D O I：

10.3934/dcdss.2024152

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

. In this paper we study the asymptotic equivalence of bounded solutions for a linear system and its perturbed system in a Banach space. We give sufficient conditions for the asymptotic equivalence by a dichotomy together with the Lipschitz property of the composition of the Green function and the perturbed term. The conditions permit that the dichotomy has different growth rates on the subspaces of the invariant decomposition and the compositions of the perturbed term and the projections have different Lipschitz constants, which are weaker than the ones in the known literatures even in the finite-dimensional case.

引用

页数：28

共 19 条

[1] NONUNIFORM EXPONENTIAL DICHOTOMIES AND ADMISSIBILITY [J].

Barreira, Luis ;

Valls, Claudia .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2011, 30 (01) :39-53

[2] ASYMPTOTIC INTEGRATION UNDER WEAK DICHOTOMIES [J].

Bodine, Sigrun ;

Lutz, D. A. .

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2010, 40 (01) :51-75

[3] ON ASYMPTOTIC RELATIONSHIPS BETWEEN SOLUTIONS OF 2 SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS [J].

BRAUER, F ;

WONG, JSW .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1969, 6 (03) :527-&

[4]

Brauer F., 1962, Mich Math J, V9, P33, DOI [10.1307/mmj/1028998618, DOI 10.1307/MMJ/1028998618]

[5]

Coppel W., 1965, Stability and Asymptotic Behavior of Differential Equations

[6]

Coppel W. A., 1978, Lecture Notes in Mathematics, V629

[7] Asymptotics for linear difference equations I: Basic theory [J].

Elaydi, S .

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 1999, 5 (06) :563-589

[8]

Hale J.K., 2013, Introduction to Functional Differential Equations, V99, DOI DOI 10.1007/978-1-4612-4342-7

[9]

Hale JK., 1980, ORDINARY DIFFERENTIA

[10]

Henry Daniel, 2006, Geometric theory of semilinear parabolic equations, V840, DOI DOI 10.1007/BFB0089647

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