Almost periodic and almost automorphic solutions of linear differential equations
type: Item
instance of: scholarly article
title: Almost periodic and almost automorphic solutions of linear differential equations
zbMATH Open document ID: 1268.37007
author: David Cheban
author: T. Caraballo
published in: Discrete and Continuous Dynamical Systems
publication date: 2013-04-24T00:00:00Z
review text: In this work the authors generalize the results of \textit{P. Cieutat} and \textit{A. Haraux} [Port. Math. (N.S.) 59, No. 2, 141--159 (2002; Zbl 1018.34049)] to the case of general linear nonautonomous dynamical systems (cocycles). More precisely, they describe the asymptotic behavior of nonautonomous linear contractive systems with minimal base and prove that, under some contracting and compactness assumptions, the associated homogeneous system either has a complete trajectory with constant positive norm, or the trivial solution is uniformly asymptotically stable. Moreover, when the second alternative holds, the nonautonomous dynamical system possesses a unique solution of the same kind as the coefficients; that is, almost periodic (resp. almost automorphic, recurrent) coefficients give rise to an almost periodic (resp. almost automorphic, recurrent) solution.
reviewed by: Matheus Cheque Bortolan
Mathematics Subject Classification ID: 37A20
Mathematics Subject Classification ID: 37B55
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 34K06
Mathematics Subject Classification ID: 34K14
Mathematics Subject Classification ID: 37B25
Mathematics Subject Classification ID: 37C75
Mathematics Subject Classification ID: 37L15
Mathematics Subject Classification ID: 37L30
Mathematics Subject Classification ID: 39A05
zbMATH DE Number: 6157281
zbMATH Keywords: almost periodic solution
zbMATH Keywords: almost automorphic solution, nonautonomous dynamical systems
zbMATH Keywords: cocycle
zbMATH Keywords: uniform asymptotic stability
zbMATH Keywords: linear nonautonomous contractive dynamical systems
MaRDI profile type: Publication
full work available at URL: dcds.2013.33.1857
OpenAlex ID: W2793911046
DOI: 10.3934/DCDS.2013.33.1857
description: scientific article; zbMATH DE number 6157281