The stability of partial difference systems with retarded arguments
type: Item
instance of: scholarly article
title: The stability of partial difference systems with retarded arguments
zbMATH Open document ID: 1053.39026
DOI: 10.1016/S0898-1221(03)00092-0
publication date: 2004-08-06T00:00:00Z
review text: The authors consider the system of partial difference equations \[ Z(x,y)=\begin{cases} \sum_{k=1}^NA_k(x,y)Z(x-p_k(x),y-q_k(y)),&x,y\in \Omega_0,\\ \varphi (x,y), &x,y\in \Omega_2,\end{cases}\tag{*} \] where \(p_k:[0,\infty )\to \mathbb R_{+}, q_k:[0,\infty )\to \mathbb R_{+},\) and \(p_k(.),q_k(.)\) are both continuous functions. \(Z,\varphi \in \mathbb R^n, A_k:\Omega _0\to \mathbb R^{n\times n}\), \(k=1,2,\dots,N,\) are real continuous functions, and \[ \Omega_0=\{(x,y)\mid x\geq 0,y\geq 0\} ,\Omega_1=\{(x,y)\mid x\geq -p,y\geq -q\} ,\Omega_2=\Omega_1/\Omega_0, \] where \(p>0,q>0\). Sufficient conditions are obtained so that the solution \(Z(x,y)\) satisfies \(\| Z(x,y)\| \to 0\). The stability of (*) has been discussed as well.
Mathematics Subject Classification ID: 39A11
zbMATH DE Number: 2082230
zbMATH Keywords: system of partial differential equations
zbMATH Keywords: delay varying in time
zbMATH Keywords: decaying solution
zbMATH Keywords: stability
author: B. G. Zhang
author: Xinghua Deng
reviewed by: Fozi Dannan
MaRDI profile type: Publication
cites work: Mathematics-teaching and research on the horns of a dilemma
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cites work: Q5690628
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2082230