A new view on one problem of asymptotic behavior of solutions of delay difference equations
type: Item
instance of: scholarly article
title: A new view on one problem of asymptotic behavior of solutions of delay difference equations
zbMATH Open document ID: 1121.39005
DOI: 10.1155/DDNS/2006/74043
author: Leonid Shaikhet
published in: Discrete Dynamics in Nature and Society
publication date: 2007-03-19T00:00:00Z
full work available at URL: https://eudml.org/doc/127981
review text: Consider the linear Volterra difference equation with real coefficients \[ x_{n+1}-x_n=ax_n+\sum_{j=1}^{\infty}K_jx_{n-j},\quad n\geq 0. \] In the first section, the author slightly generalizes an asymptotic result obtained by \textit{I.-G. E. Kordonis} and \textit{C. G. Philos} [J. Differ. Equations Appl. 5, No. 3, 219--233 (1999; Zbl 0973.39005)], where a stability criterion is derived via a positive root of the corresponding characteristic equation. In addition, a new generalization is developed for the second-order linear difference equation \[ x_{n+1}-x_n=ax_n+b x_{n-1}. \] The author suggests that similar ideas might be applied for a general Volterra difference equation and also for functional-differential equations.
reviewed by: Shangjiang Guo
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 5134609
zbMATH Keywords: delay
zbMATH Keywords: asymptotics
zbMATH Keywords: linear Volterra difference equation
zbMATH Keywords: stability
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5134609