Local mild solutions and impulsive mild solutions for semilinear Cauchy problems involving lower Scorza-Dragoni multifunctions
type: Item
instance of: scholarly article
title: Local mild solutions and impulsive mild solutions for semilinear Cauchy problems involving lower Scorza-Dragoni multifunctions
zbMATH Open document ID: 1193.34123
author: Tiziana Cardinali
author: Francesco Portigiani
author: Paola Rubbioni
published in: Topological Methods in Nonlinear Analysis
publication date: 2009-06-23T00:00:00Z
review text: The authors consider the semilinear differential inclusion \[ x'\in A(t)x+F(t,x),\qquad x(0)=x_0\tag{1} \] in a Banach space, where {A(t)} is a family of linear operators generating an evolution system, and F is a set-valued function satisfying the lower Scorza-Dragoni property. The authors first prove a Carathéodory selection theorem, which is an extension of the one in [\textit{Z. Artstein} and \textit{K. Prikry}, J. Math. Anal. Appl. 127, 540--547 (1987; Zbl 0649.28011)]. Applying this result and known existence theorems, the authors prove several theorems on the existence of local and global mild solutions to problem (1), and also existence of mild solutions to an impulsive version of (1). A closely related paper is [\textit{G. Bezzini} and \textit{T. Cardinali}, ``Local mild solutions for semilinear evolution differential inclusions with lower semicontinuous type multifunctions'', P. U. M. A. 18, 1--17 (2007)].
reviewed by: Daniel C. Biles
Mathematics Subject Classification ID: 34G25
Mathematics Subject Classification ID: 34A37
Mathematics Subject Classification ID: 26E25
Mathematics Subject Classification ID: 34A12
zbMATH DE Number: 5567741
zbMATH Keywords: differential inclusion
zbMATH Keywords: semilinear
zbMATH Keywords: Scorza-Dragoni
zbMATH Keywords: selection
zbMATH Keywords: mild solution
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5567741