On the uniform asymptotic stability for a linear integro-differential equation of Volterra type
type: Item
instance of: scholarly article
title: On the uniform asymptotic stability for a linear integro-differential equation of Volterra type
zbMATH Open document ID: 1105.45009
author: Minoru Funakubo
author: Sadahisa Sakata
author: T. Hara
published in: Journal of Mathematical Analysis and Applications
publication date: 2006-11-15T00:00:00Z
review text: The paper deals with the following linear integro-differential equation of Volterra type: \[ \dot{x}(t) = a x(t) - b \int_{t-h}^t x(s) ds, \] with \(a, b\) real numbers and \(h>0\). The authors consider here only the case of \(a>0\), and study the uniform asymptotic stability of the zero solution to this equation. By using the root analysis of the characteristic equation, a necessary and sufficient condition for asymptotic stability is proved.
Mathematics Subject Classification ID: 45M10
Mathematics Subject Classification ID: 45M05
Mathematics Subject Classification ID: 45J05
zbMATH DE Number: 5073003
zbMATH Keywords: characteristic equation
zbMATH Keywords: delay
zbMATH Keywords: linear integro-differential equation of Volterra type
zbMATH Keywords: uniform asymptotic stability
reviewed by: Iulian Stoleriu
MaRDI profile type: Publication
full work available at URL: j.jmaa.2005.12.053
OpenAlex ID: W2074417637
Wikidata QID: Q115346285
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DOI: 10.1016/J.JMAA.2005.12.053
description: scientific article; zbMATH DE number 5073003