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March  2006, 5(1): 107-124. doi: 10.3934/cpaa.2006.5.107

On the strong invariance property for non-Lipschitz dynamics

Mikhail Krastanov 1, , Michael Malisoff 2, and  Peter Wolenski 2,

1. 

Department of Biomathematics, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev str., bl 8, 1113 Sofia, Bulgaria
2. 

Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803-4918, United States, United States

Received  March 2005 Revised  August 2005 Published  December 2005

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: nonsmooth analysis., Invariance.
Mathematics Subject Classification: Primary: 34A60; Secondary: 34D0.
Citation: Mikhail Krastanov, Michael Malisoff, Peter Wolenski. On the strong invariance property for non-Lipschitz dynamics. Communications on Pure & Applied Analysis, 2006, 5 (1) : 107-124. doi: 10.3934/cpaa.2006.5.107
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