Differential inclusions with constraints in Banach spaces
type: Item
instance of: scholarly article
title: Differential inclusions with constraints in Banach spaces
zbMATH Open document ID: 1028.34056
DOI: 10.12775/TMNA.2002.028
author: Aleksander Ćwiszewski
published in: Topological Methods in Nonlinear Analysis
publication date: 2004-01-13T00:00:00Z
review text: Here, the author investigates the topological properties of the solution set to a constrained differential inclusion of the form \[ \dot{u}(t)\in F(t,u(t))\text{ a.e. on } I=[0,1],\;f(u(t))\leq 0,\;u(0)=u_0 \] with \(F:I\times U\to 2^{E}\) and \(U\) an open subset of a Banach space \(E\). By assuming that the multivalued term is upper semicontinuous, satisfies a compactness condition (formulated by Kuratowski's measure of noncompactness) and a tangency condition (expressed with the help of Clarke's tangent cone), he proves that the solution set is \(R_\delta\) in \(C(I,E)\). Moreover, he applies this result to investigate the structure of the viable solution set. This way, he generalizes several earlier obtained results.
reviewed by: Nikos Yannakakis
Mathematics Subject Classification ID: 34G25
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34G20
zbMATH DE Number: 1869657
zbMATH Keywords: upper semicontinuous multifuncion
zbMATH Keywords: set-valued map
zbMATH Keywords: differential inclusion
zbMATH Keywords: Kuratowski's measure of noncompactness
zbMATH Keywords: Clarke's tangent cone
zbMATH Keywords: generalized gradient
zbMATH Keywords: Clarke's derivative
zbMATH Keywords: viable solution
zbMATH Keywords: solution set
zbMATH Keywords: topological structure
zbMATH Keywords: functional constraints
Wikidata QID: Q96744729
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1869657