Weak flow-invariance for non-convex differential inclusions
type: Item
instance of: scholarly article
title: Weak flow-invariance for non-convex differential inclusions
zbMATH Open document ID: 0757.34017
published in: Differential and Integral Equations
publication date: 1993-01-16T00:00:00Z
review text: By using the Scorza Dragoni property the technique of directionally continuous selections [see \textit{A. Bressan}, Directionally continuous selections and differential inclusions, Funkc. Ekvacioj, Ser. Int. 31, No. 3, 459-470 (1988; Zbl 0676.34014)] is adapted to the Carathéodory lower semicontinuous, integrably bounded, closed valued multifunction \(F(t,x)\) and then, by the construction of polygonal approximations, the existence of a viable solution \(x(t)\in K\) for \(\dot x(t)\in F(T,x(t))\) is shown in the case when \(K\) is a locally compact subset of a reflexive Banach space and the function \(F\) satisfies the classical tangency condition: \(F(t,x)\) being contained in Bouligand's contingent cone \(T_ K(x)\).
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34C11
zbMATH DE Number: 90482
zbMATH Keywords: Cauchy problem
zbMATH Keywords: differential inclusion
zbMATH Keywords: Scorza Dragoni property
zbMATH Keywords: viable solution
zbMATH Keywords: reflexive Banach space
zbMATH Keywords: Bouligand's contingent cone
author: Giovanni Colombo
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 90482