Existence results for a class of abstract nonlocal Cauchy problems
type: Item
instance of: scholarly article
title: Existence results for a class of abstract nonlocal Cauchy problems
zbMATH Open document ID: 0954.34055
DOI: 10.1016/S0362-546X(98)00227-2
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2001-01-23T00:00:00Z
review text: The authors study the global existence of a solution to nonlinear evolution equations with nonlocal conditions of the form \[ u'(t) + Au(t) \ni f(t,u(t)), \quad u(0)=g(u), \quad 0<t<T, \tag{*} \] in a real Banach space \(X\). Here, \(A\) is a nonlinear \(m\)-accretive (possibly multivalued) operator on \(X\), \(F: L^1(0,T;X) \to L^1(0,T;X)\) and \(g:L^1(0,T;X) \to \overline {D(A)}\). Using the Schauder fixed point theorem, the Fryszkowski selection theorem and some properties of compact semigroups, the authors prove the existence of integral solutions. This work is a continuation of the paper by \textit{S. Aizicovici} and \textit{Y. Gao} [J. Appl. Math. Stochastic Anal. 10, No.~2, 145-156 (1997; Zbl 0883.34065)].
reviewed by: Józef Myjak
Mathematics Subject Classification ID: 34G25
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 47H06
zbMATH DE Number: 1389683
zbMATH Keywords: nonlocal initial condition
zbMATH Keywords: \(m\)-accretive operator
zbMATH Keywords: compact semigroup
zbMATH Keywords: integral solution
author: Sergiu Aizicovici
author: Mark McKibben
MaRDI profile type: Publication
Wikidata QID: Q127840470
full work available at URL: s0362-546x(98)00227-2
OpenAlex ID: W2075561277
description: scientific article; zbMATH DE number 1389683