Existence results for nonlinear integral equations
type: Item
instance of: scholarly article
title: Existence results for nonlinear integral equations
zbMATH Open document ID: 0851.45003
author: Donal O'Regan
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-11-26T00:00:00Z
review text: The author gives sufficient conditions for the existence of a solution of the nonlinear Volterra integral equation \[ y(t)= h(t)+ \int^t_0 k(t, s) f(s, y(s)) ds, \qquad 0\leq t<T, \] and for the Hammerstein integral equation \[ y(t)= h(t)+ \int^1_0 k(t, s) f(s, y(s)) ds, \qquad 0\leq t\leq 1, \] using the Schauder-Tychonoff fixed-point theorem and a nonlinear alternative of Leray-Schauder type. For the Volterra equation both the case of a continuous solution and the case where the solution belongs locally to an \(L^p\)-space are considered and the solutions are not only local ones but guaranteed to exist on the whole interval \([0, T)\). The existence of solutions of the Hammerstein equation are obtained under assumptions (that in some cases are quite complicated) involving monotonicity of \(k\) and \(f\).
reviewed by: Gustaf Gripenberg
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 811158
zbMATH Keywords: Lp-solution
zbMATH Keywords: nonlinear Volterra integral equation
zbMATH Keywords: Hammerstein integral equation
zbMATH Keywords: continuous solution
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1199
OpenAlex ID: W1983725570
DOI: 10.1006/JMAA.1995.1199
description: scientific article; zbMATH DE number 811158