Asymptotic behavior of solutions of functional difference equations
type: Item
instance of: scholarly article
title: Asymptotic behavior of solutions of functional difference equations
zbMATH Open document ID: 1074.39009
author: H. Matsunaga
author: Satoru Murakami
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-04-28T00:00:00Z
review text: The authors consider a difference equation of the form \(x(n+1)=L(x_{n})+G(n)x_{n}\) where \(L\) is a bounded linear operator defined on a linear space and \(G(n)\) also is a bounded linear operator defined on a complex space. They investigate the asymptotic behavior of the solution under the condition \(\lim_{n\rightarrow \infty }\left\| G(n)\right\| =0\), where \(\left\| .\right\|\) is the operator norm of \(G(n).\) Some auxiliary lemmas that are used in the proof of the main results are stated and proved. The results are applied to different types of Volterra difference equations and the asymptotic behavior of their solutions are given. The results can be considered as the extension of the results given by \textit{M. Pituk} [J. Difference Equ. Appl. 8, No. 3, 201--216 (2002; Zbl 1002.39014)].
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 2162009
zbMATH Keywords: functional difference equations
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: phase space
zbMATH Keywords: Volterra difference equations
zbMATH Keywords: delay
reviewed by: S. H. Saker
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.10.065
OpenAlex ID: W2027650677
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DOI: 10.1016/J.JMAA.2004.10.065
description: scientific article; zbMATH DE number 2162009