Work

Dichotomy and asymptotic equivalence of bounded solutions for systems in Banach spaces

Year: 2024

Type: article

Abstract: 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.

Source: Discrete and Continuous Dynamical Systems - S

DOI: 10.3934/dcdss.2024152

Authors: Yujie Bai, Haiyang Huang, Linfeng Zhou

Institution: Sichuan University

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4402007937

FWCI:

Cites: 12

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Related to: 10