Perturbation of linear abstract Volterra equations
type: Item
instance of: scholarly article
title: Perturbation of linear abstract Volterra equations
zbMATH Open document ID: 0824.45013
published in: Journal of Integral Equations and Applications
publication date: 1995-08-13T00:00:00Z
review text: The aim of this paper is to discuss perturbed equations associated with abstract Volterra equations. We will consider only the case when the unperturbed equation is linear, namely, (1) \(x(t)= (Lx)(t)+ (Nx)(t)\), or (2) \(\dot x(t)= (Lx)(t)+ (Nx)(t)\). In both equations (1) and (2), \(L\) stands for a linear abstract Volterra operator acting on some function space, while \(N\) denotes a nonlinear operator acting on the same or another function space, not necessarily of Volterra type. Of course, when \(N\) is also a Volterra (abstract) operator, the equations (1) and (2) are both of Volterra type.
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 45J05
zbMATH DE Number: 784746
zbMATH Keywords: qualitative theory of Volterra equations
zbMATH Keywords: nonconvolution equations
zbMATH Keywords: resolvent kernel
zbMATH Keywords: perturbation theory of integral/integro-differential equations
zbMATH Keywords: abstract Volterra equations
zbMATH Keywords: linear abstract Volterra operator
zbMATH Keywords: nonlinear operator
author: Constantin Corduneanu
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/jiea/1181075570
OpenAlex ID: W2094984783
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DOI: 10.1216/JIEA/1181075570
description: scientific article; zbMATH DE number 784746