Random extremal solutions of differential inclusions

Alberto Bressan, Vasile Staicu

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Given a Lipschitz continuous multifunction F on (Formula presented.) , we construct a probability measure on the set of all solutions to the Cauchy problem (Formula presented.) with x(0) = 0. With probability one, the derivatives of these random solutions take values within the set extF(x) of extreme points for a.e. time t. This provides an alternative approach in the analysis of solutions to differential inclusions with non-convex right hand side.

Original languageEnglish (US)
Article number23
JournalNonlinear Differential Equations and Applications
Volume23
Issue number3
DOIs
StatePublished - Jun 1 2016

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Extremal Solutions
Differential Inclusions
Extreme Points
Probability Measure
Lipschitz
Cauchy Problem
Derivatives
Derivative
Alternatives

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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abstract = "Given a Lipschitz continuous multifunction F on (Formula presented.) , we construct a probability measure on the set of all solutions to the Cauchy problem (Formula presented.) with x(0) = 0. With probability one, the derivatives of these random solutions take values within the set extF(x) of extreme points for a.e. time t. This provides an alternative approach in the analysis of solutions to differential inclusions with non-convex right hand side.",
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Random extremal solutions of differential inclusions. / Bressan, Alberto; Staicu, Vasile.

In: Nonlinear Differential Equations and Applications, Vol. 23, No. 3, 23, 01.06.2016.

Research output: Contribution to journalArticle

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