Weak tangency, weak invariance, and Carathéodory mappings
type: Item
instance of: scholarly article
title: Weak tangency, weak invariance, and Carathéodory mappings
zbMATH Open document ID: 1025.34057
DOI: 10.1023/A:1020765401015
published in: Journal of Dynamical and Control Systems
publication date: 2002-12-15T00:00:00Z
review text: The authors obtain new results on weak invariance in Hilbert spaces both in autonomous and nonautonomous case. First, they consider a multifunction from a Hilbert space \(H\) to nonempty subsets of \(H\) which is upper hemicontinuous and satisfies a growth condition and they give necessary and sufficient conditions for a subset \(S\) of \(H\) to be approximately weakly invariant with respect to approximate solutions to the differential inclusion \(\dot{x}(t) \in F(x(t))\). Then, they consider also the nonautonomous case in which the multifunction is defined on \([a,b) \times H\) into \(H\) and they extend the previous result to the case where the multifunction is of Carathéodory type. In the final part, some applications are presented.
reviewed by: Francesca Papalini
Mathematics Subject Classification ID: 34G25
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 34G20
zbMATH DE Number: 1845285
zbMATH Keywords: nonautonomous differential inclusions
zbMATH Keywords: weak invariance
zbMATH Keywords: weak tangency
zbMATH Keywords: strong invariance
zbMATH Keywords: Carathéodory mappings
zbMATH Keywords: viability
zbMATH Keywords: Lebesgue derivation
author: Ovidiu Cârjă
author: M. D. P. Monteiro Marques
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1845285