Pseudo almost-periodic solutions to systems of differential equations with piecewise constant argument \([t]\)
type: Item
instance of: scholarly article
title: Pseudo almost-periodic solutions to systems of differential equations with piecewise constant argument \([t]\)
zbMATH Open document ID: 1011.34062
DOI: 10.1007/BF02877433
published in: Science in China. Series A
publication date: 2002-08-15T00:00:00Z
review text: The author considers the system of differential equations with piecewise constant argument \[ \dot x(t)= Ax(t)+ Bx([t])+ f(t),\quad t\in\mathbb{R},\tag{1} \] and the nonlinear system with piecewise constant argument \[ \dot x(t)= Ax(t)+ Bx([t])+ f(t)+ \mu F(t,x),\quad t\in\mathbb{R},\tag{2} \] where \(A\), \(B\) are constant matrices and \(A\) is nonsingular (\([\cdot]\) denotes the greatest-integer function). The author introduces a generalization of almost-periodic vector sequences (he calls them pseudo almost-periodic vector sequences). Thus, by constructing pseudo almost-periodic sequence solutions for a system of difference equations, he investigates the existence of pseudo almost-periodic solutions to systems (1) and (2). He also proves that under certain conditions the solution is unique.
Mathematics Subject Classification ID: 34K14
Mathematics Subject Classification ID: 34K06
zbMATH DE Number: 1782153
zbMATH Keywords: pseudo almost-periodic functions
zbMATH Keywords: piecewise constant arguments
author: Daxiong Piao
reviewed by: V. Petrov
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02877433
OpenAlex ID: W4234923944
description: scientific article; zbMATH DE number 1782153