An application of a diffeomorphism theorem to Volterra integral operator.
type: Item
instance of: scholarly article
title: An application of a diffeomorphism theorem to Volterra integral operator.
zbMATH Open document ID: 1463.45056
author: Josef Diblík
author: Marek Galewski
author: Marcin Koniorczyk
author: Ewa Schmeidel
published in: Differential and Integral Equations
publication date: 2018-06-15T00:00:00Z
review text: This paper studies Volterra operators \[V(x)(t)=x(t)+\int_0^t v(t,\tau,x(\tau))d\tau,\] on the space \(\tilde{W}_0^{1,p}([0,1],\mathbb{R}^n)\) of absolutely continuous functions \(x\) with \(x'\in L^p\) and \(x(0)=0\). Under appropriate assumptions on the function \(v\), it is proved, using a global diffeomorphism theorem, that the operator \(V\) is a diffeomorphism. This provides existence and uniqueness of the solution of the equation \(V(x)=y\), as well as its smooth dependence on \(y\).
reviewed by: Guy Katriel
Mathematics Subject Classification ID: 45P05
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 26B10
Mathematics Subject Classification ID: 47J07
zbMATH DE Number: 6890407
zbMATH Keywords: Volterra equation
zbMATH Keywords: global diffeomorphism theorem
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6890407