Volterra integral inclusions in Banach spaces
type: Item
instance of: scholarly article
title: Volterra integral inclusions in Banach spaces
zbMATH Open document ID: 0659.45010
DOI: 10.1216/JIE-1988-1-1-65
author: Nikolaos S. Papageorgiou
published in: Journal of Integral Equations and Applications
publication date: 1988-01-01T00:00:00Z
review text: The author proves the existence of a solution of the integral inclusion \[ x(t)\in p(t)+\int^{t}_{0}K(t,s)F(s,x(s))ds \] in a separable Banach space X under the assumptions that F(t,x) is a compact set in X for each t and x, the function \(x\mapsto F(t,x)\) is Hausdorff continuous, and F satisfies a standard condition concerning the measure of noncompactness. It is stressed that no assumptions involving convexity are involved. Some special kinds of solutions (like extremal solutions and quasitrajectories) are examined as well. Some results concerning weak convergence and a set-valued version of Fatou's lemma are established.
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 45D05
zbMATH DE Number: 4077979
zbMATH Keywords: Volterra equation
zbMATH Keywords: integral inclusion
zbMATH Keywords: Banach space
zbMATH Keywords: measure of noncompactness
zbMATH Keywords: extremal solutions
zbMATH Keywords: quasitrajectories
zbMATH Keywords: weak convergence
reviewed by: Gustaf Gripenberg
MaRDI profile type: Publication
full work available at URL: jie-1988-1-1-65
OpenAlex ID: W1974708291
description: scientific article; zbMATH DE number 4077979