On the order of exponential growth of the solution of the linear difference equation with periodic coefficient in Banach space
type: Item
instance of: scholarly article
title: On the order of exponential growth of the solution of the linear difference equation with periodic coefficient in Banach space
zbMATH Open document ID: 0574.39002
DOI: 10.1155/S0161171285000424
author: H. Attia Hussein
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/45971
review text: Denote by \(E_{\alpha}\) the set of all elements f(t) of a Banach space E such that \(\sup \{\| f(t)\| \exp (-\alpha t)\}<\infty\) and let A(t)\(\in {\mathcal L}(E)\) be such that \(A(t+\omega)=A(t)\). The author proves the following theorem: If \(f\in E_{\alpha}\), then the solution y of equation \(\Delta y-A(t)y=f(t)\), \(t\geq \delta\), where \(\Delta y=(y(t+\delta)-y(t))/\delta\), \(\delta >0\), belongs to \(E_{\beta}\) such that \(\beta =\alpha\), when \(\alpha >\alpha_ 0\), \(\beta >\alpha\), when \(\alpha =\alpha_ 0\), \(\beta =\alpha_ 0\), when \(\alpha <\alpha_ 0\) \((\alpha_ 0=(\ln | \lambda_ 0| /\omega\), \(\lambda_ 0\in \sigma_ B\), \(B=\prod^{0}_{k=\omega -1}[I+A(k)])\).
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 3916885
zbMATH Keywords: difference equations
zbMATH Keywords: solution of exponential growth
zbMATH Keywords: Banach space
reviewed by: Pavel Talpalaru
MaRDI profile type: Publication
OpenAlex ID: W1985452059
description: scientific article; zbMATH DE number 3916885