Time dependent Desch-Schappacher type perturbations of Volterra integral equations
type: Item
instance of: scholarly article
title: Time dependent Desch-Schappacher type perturbations of Volterra integral equations
zbMATH Open document ID: 1032.45016
DOI: 10.1007/BF01193674
author: Yanyan Li
published in: Integral Equations and Operator Theory
publication date: 2004-03-13T00:00:00Z
review text: The authors study perturbations of the Volterra integral equation \[ u(t)=f(t)+ \int_0^t a(t-s)Au(s) ds, \quad t\geq 0, \] where \(A\) is a closed linear operator in a Banach space and where it is assumed that there is a strongly continuous resolvent for the equation. The perturbations are either multiplicative, i.e., \(u(t)=f(t)+\int_0^t a(t-s)B(s)Au(s) ds\) or additive, i.e., \(u(t)=f(t)+\int_0^t a(t-s)(B(s)+A)u(s) ds\). In both cases the authors first prove a more general result with complicated assumptions and then in a series of corollaries give simple and sufficient conditions for the assumptions of the general theorem to hold.
reviewed by: Gustaf Gripenberg
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 45D05
zbMATH DE Number: 1890565
zbMATH Keywords: Volterra integral equation
zbMATH Keywords: perturbation
zbMATH Keywords: Banach space
MaRDI profile type: Publication
cites work: Q3830008
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description: scientific article; zbMATH DE number 1890565