On semilinear differential inclusions with lower semicontinuous nonlinearities
type: Item
instance of: scholarly article
title: On semilinear differential inclusions with lower semicontinuous nonlinearities
zbMATH Open document ID: 1035.34066
DOI: 10.1007/BF02505897
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2003-09-24T00:00:00Z
review text: The authors study a Cauchy problem governed by the semilinear differential inclusion in a Banach space \[ x'(t)\in Ax(t)+F(t,x(t)), \;t\in [0,a], \] where the linear operator \(A:D(A)\subset E\to E\) is the infinitesimal generator of a strongly continuous semigroup and \(F\) is a lower semicontinuous multifunction not necessarily convex-valued. In this general situation, the authors prove the existence of a mild solution to the problem. They make use of a technique developed by themselves and based on the notion of measure of noncompactness.
reviewed by: Paola Rubbioni
Mathematics Subject Classification ID: 34G25
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 47Hxx
zbMATH DE Number: 1985420
zbMATH Keywords: measure of noncompactness
zbMATH Keywords: semilinear differential inclusions
zbMATH Keywords: Banach spaces
author: Mikhail Kamenskii
author: Valerii V. Obukhovskij
author: Pietro Zecca
MaRDI profile type: Publication
cites work: Multivalued mappings
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cites work: ON SOLUTIONS OF A DIFFERENTIAL INCLUSION WITH LOWER SEMICONTINUOUS NONCONVEX RIGHT-HAND SIDE IN A BANACH SPACE
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description: scientific article; zbMATH DE number 1985420