On bounded solutions of a difference equation with jumps of the operator coefficient
type: Item
instance of: scholarly article
title: On bounded solutions of a difference equation with jumps of the operator coefficient
zbMATH Open document ID: 1394.39004
author: M. F. Horodnii
author: I. V. Honchar
published in: Journal of Mathematical Sciences (New York)
publication date: 2018-03-28T00:00:00Z
review text: The authors study the difference equations \[ x_{n+1}=Ax_n+y_n,\;\;n\geq 1, \] \[ x_{n+1}=Bx_n+y_n,\;\;n\leq 0, \] on a finite-dimensional complex Banach space \(X\). They obtain necessary and sufficient conditions for the operators \(A\) and \(B\) such that for any bounded sequence \(\{y_n, n\in \mathbb{Z}\}\) in \(X\), the above difference equations have a unique bounded solution \(\{x_n, n\in \mathbb{Z}\}\) in the space \(X\).
reviewed by: Fei Xue
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 39A22
zbMATH DE Number: 6854261
zbMATH Keywords: difference equation
zbMATH Keywords: bounded solution
zbMATH Keywords: unique solution
MaRDI profile type: Publication
full work available at URL: s10958-018-3685-4
OpenAlex ID: W2793592085
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DOI: 10.1007/S10958-018-3685-4
description: scientific article; zbMATH DE number 6854261