Extremal solutions of differential inclusions via Baire category: A dual approach

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Abstract

Let F be a continuous multifunction on Rn with compact convex values. For any vector w, let Fw(x)⊆F(x) be the subset of points which maximize the inner product with w. Call W the set of all continuous functions w:[0,T]{mapping}Rn with the following property: all solutions to the Cauchy problem ẋ(t)∈Fw(t)(x(t)), x(0) = 0, are also solutions to ẋ(t)∈extF(x(t)). We prove that W is residual in C([0,T]; Rn).

Original languageEnglish (US)
Pages (from-to)2392-2399
Number of pages8
JournalJournal of Differential Equations
Volume255
Issue number8
DOIs
StatePublished - Oct 15 2013

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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