Well posedness for differential inclusions on closed sets
type: Item
instance of: scholarly article
title: Well posedness for differential inclusions on closed sets
zbMATH Open document ID: 0731.34012
DOI: 10.1016/0022-0396(91)90060-M
author: Arrigo Cellina
author: Vasile Staicu
published in: Journal of Differential Equations
publication date: 1991-01-01T00:00:00Z
review text: Extending previous results, the authors prove a theorem stating the existence of a continuous selection \(y\mapsto x(.;y)\in AC([0,T];{\mathbb{R}}^ n),\) of solutions remaining on a closed subset \(K\subset {\mathbb{R}}^ n\), of a differential inclusion \(x'\in F(t,x)\), \(x(0)=y\in K\), in the case F(.,.) has closed nonempty values, is of Carathéodory-Lipschitz type and satisfies the Nagumo tangential condition: \(F(t,x)\subset T_ K(x)\forall (t,x)\in [0,T]\times K\), where \(T_ K(x)\) denotes the contingent cone to K at \(x\in K\). As corollaries of the theorem, the arcwise connectedness of the set of solutions and of the attainable sets is obtained.
Mathematics Subject Classification ID: 34A60
zbMATH DE Number: 4208528
zbMATH Keywords: differential inclusions on closed sets
zbMATH Keywords: well posed problems
zbMATH Keywords: tangent cones
zbMATH Keywords: Carathéodory-Lipschitz type
zbMATH Keywords: Nagumo tangential condition
reviewed by: Ştefan Mirică
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4208528