Almost periodic solutions of Volterra equations and attractivity
type: Item
instance of: scholarly article
title: Almost periodic solutions of Volterra equations and attractivity
zbMATH Open document ID: 0856.45010
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-02-24T00:00:00Z
review text: Consider the system of nonlinear integral equations \[ x(t) = a(t) + \int^t_\alpha D \bigl( t,s,x (s) \bigr) ds, \tag{1} \] where \(\alpha\) is either finite or \(- \infty\), and the related system of limiting equations \[ x(t) = p(t) + \int^t_{- \infty} P \bigl( t,s,x (s) \bigr) ds. \tag{2} \] The function \(a\) is asymptotically almost periodic with almost periodic part \(p\), and the two functions \(D\) and \(P\) are related to each other in a similar manner. The paper contains several results on the relation between the solutions of these two equations. Among others, it is shown that a unique bounded solution of (2) must be almost periodic and a unique bounded solution of (1) must be asymptotically almost periodic, and that the two solutions have the same almost periodic part. The existence, uniqueness, and attractivity of an (asymptotically) almost periodic solution is also studied.
Mathematics Subject Classification ID: 45G15
Mathematics Subject Classification ID: 45M10
Mathematics Subject Classification ID: 45M15
zbMATH DE Number: 902519
zbMATH Keywords: system of nonlinear integral equations
zbMATH Keywords: attractivity
zbMATH Keywords: almost periodic solution
author: T. A. Burton
author: Tetsuo Furumochi
reviewed by: Olof Staffans
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0100
OpenAlex ID: W1979075192
DOI: 10.1006/JMAA.1996.0100
description: scientific article; zbMATH DE number 902519