Stability properties and integrability of the resolvent of linear Volterra equations
type: Item
instance of: scholarly article
title: Stability properties and integrability of the resolvent of linear Volterra equations
zbMATH Open document ID: 0826.45004
author: Paul W. Eloe
author: Muhammad Nazmul Islam
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1995-12-03T00:00:00Z
review text: Integrability of the resolvent and the stability properties of the zero solution of linear Volterra integrodifferential equations are studied. In particular, it is shown that the zero solution is uniformly stable if and only if the resolvent is integrable in some sense. It is also shown that the zero solution is uniformly asymptotically stable if and only if the resolvent is integrable and an additional condition in terms of the resolvent and the kernel is satisfied. Finally, the integrability of the resolvent is obtained under an explicit condition.
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45M10
zbMATH DE Number: 794317
zbMATH Keywords: asymptotic stability
zbMATH Keywords: stability
zbMATH Keywords: linear Volterra integrodifferential equations
zbMATH Keywords: integrability of the resolvent
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178225595
OpenAlex ID: W2034186080
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DOI: 10.2748/TMJ/1178225595
description: scientific article; zbMATH DE number 794317