On the strong invariance property for non-lipschitz dynamics
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.
Publication Source (Journal or Book title)
Communications on Pure and Applied Analysis
Krastanov, M., Malisoff, M., & Wolenski, P. (2006). On the strong invariance property for non-lipschitz dynamics. Communications on Pure and Applied Analysis, 5 (1), 107-124. https://doi.org/10.3934/cpaa.2006.5.107