On bounded solutions of some classes of two-parameter difference equations in a Banach space
type: Item
instance of: scholarly article
zbMATH Open document ID: 0974.39002
publication date: 2001-08-08T00:00:00Z
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 1631381
zbMATH Keywords: difference equation
zbMATH Keywords: bounded solution
MaRDI profile type: Publication
author: M. F. Gorodnij
author: O. A. Lagoda
title: On bounded solutions of some classes of two-parameter difference equations in a Banach space
published in: Ukraïns'kyĭ Matematychnyĭ Zhurnal
review text: The authors study some classes of difference equations for vector-valued functions, for example, the equation NEWLINE\[NEWLINE u(m,n)=Au(m,n-1)+Bu(m-1,n)+Cu(m-1,n-1)+v(m,n),\;\;m\geq 1,\;n\geq 1, NEWLINE\]NEWLINE where \(A,B,C\) are bounded operators and the vector-functions \(v(m,n)\), \(u(m,0)\), \(u(0,n)\) are given. Necessary and sufficient conditions for the existence and uniqueness of a bounded solution are proposed.
reviewed by: Anatoly N. Kochubei
description: scientific article; zbMATH DE number 1631381