Function bounds for solutions of Volterra equations and exponential asymptotic stability
type: Item
instance of: scholarly article
title: Function bounds for solutions of Volterra equations and exponential asymptotic stability
zbMATH Open document ID: 1117.45003
author: L. C. Becker
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2007-05-15T00:00:00Z
review text: The main purpose of this paper is to obtain functions that bound the solutions of the scalar linear Volterra integro-differential equation \[ x'(t)=-a(t)x(t)+\int_0^tb(t-s)x(s)ds, \] where \(a,b:[0,\infty)\to {\mathbb R}\) are continuous functions and \(b\) is nonnegative. In order to achieve this purpose an extension of Gronwall's inequality is derived. The obtained bound functions are then used to find conditions that drive its solutions to zero, and to obtain conditions under which the zero solution is exponentially asymptotically stable.
reviewed by: Sotiris K. Ntouyas
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45M10
Mathematics Subject Classification ID: 26D10
Mathematics Subject Classification ID: 45M05
zbMATH DE Number: 5152800
zbMATH Keywords: exponential asymptotic stability
zbMATH Keywords: function bounds
zbMATH Keywords: Gronwall's inequality
zbMATH Keywords: variation of parameters
zbMATH Keywords: linear Volterra integro-differential equation
MaRDI profile type: Publication
full work available at URL: j.na.2006.05.016
OpenAlex ID: W2038831141
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DOI: 10.1016/J.NA.2006.05.016
description: scientific article; zbMATH DE number 5152800