On the strong invariance property for non-Lipschitz dynamics

Mikhail Krastanov; Michael Malisoff; Peter Wolenski

doi:10.3934/cpaa.2006.5.107

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2006, Volume 5, Issue 1: 107-124. Doi: 10.3934/cpaa.2006.5.107

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On the strong invariance property for non-Lipschitz dynamics

1.
Department of Biomathematics, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev str., bl 8, 1113 Sofia
2.
Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803-4918

Received: February 28, 2005

Revised: July 31, 2005

Published: February 2006

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Abstract

We provide a new sufficient condition for strong invariance for differential inclusions, under very general conditions on the dynamics, in terms of a Hamiltonian inequality. In lieu of the usual Lipschitzness assumption on the multifunction, we assume a feedback realization condition that can in particular be satisfied for measurable dynamics that are neither upper nor lower semicontinuous.

Keywords:

Invariance,
nonsmooth analysis.

Mathematics Subject Classification: Primary: 34A60; Secondary: 34D05.

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