Boundedness and almost periodicity of solutions of linear differential systems
type: Item
instance of: scholarly article
title: Boundedness and almost periodicity of solutions of linear differential systems
author: D. Lassoued
author: Michal Fečkan
published in: Mathematica Slovaca
publication date: 2022-10-19T00:00:00Z
review text: In this paper there is investigated the system \[ x^{\prime}= A(t)x+b(t),\quad t\in \mathbb{R}, \] where \(b:\mathbb{R}\to \mathbb{R}^n\) is an almost periodic function and \(A\) is an \(n\times n\)-matrix that is almost periodic. The authors prove that if all solutions of the corresponding homogeneous system are almost periodic, then there is an almost periodic function \(b\) for which the considered nonhomogeneous system has no bounded solutions. Moreover, in the paper it is proved that if for any almost periodic function \(b\) there is a bounded solution of the considered nonhomogeneous function, then there is at least one solution of the corresponding homogeneous system that is not almost periodic.
reviewed by: Svetlin Georgiev
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34C27
Mathematics Subject Classification ID: 34C11
zbMATH DE Number: 7604037
zbMATH Keywords: almost periodic solutions
zbMATH Keywords: boundedness
MaRDI profile type: Publication
full work available at URL: ms-2022-0082
OpenAlex ID: W4312382373
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DOI: 10.1515/MS-2022-0082
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description: scientific article; zbMATH DE number 7604037