On the set of solutions to Lipschitzian differential inclusions
type: Item
instance of: scholarly article
title: On the set of solutions to Lipschitzian differential inclusions
zbMATH Open document ID: 0723.34009
author: Arrigo Cellina
published in: Differential and Integral Equations
publication date: 1988-01-01T00:00:00Z
review text: We consider a Lipschitzian differential inclusion \((1)\quad x'(t)\in F(t,x),\quad x(t_ 0)=a,\) where the values of F are compact but not convex. We prove that the map that associates to the initial point a the set of solutions to (1), \(S_ F(a)\), admits a selection, continuous from \(R^ n\) to the space of absolutely continuous functions. The images of this map are sets that are not decomposable. In particular, the map from a to the attainable set at T, \(A_ T(a)\), admits a continuous selection. It is known that this map, in general, has no closed values.
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 93B03
zbMATH DE Number: 4192142
zbMATH Keywords: Lipschitzian differential inclusion
zbMATH Keywords: compact but not convex
zbMATH Keywords: continuous selection
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description: scientific article; zbMATH DE number 4192142