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We study discrete approximations of nonconvex differential inclusions in Hilbert spaces and dynamic optimization/optimal control problems involving such differential inclusions and their discrete approximations. The underlying feature of the problems under consideration is a modified one-sided Lipschitz condition imposed on the right-hand side (i.e., on the(More)
In the paper some known and new extensions of the famous theorem of Filippov (1967) and a theorem of Pliś (1965) for differential inclusions are presented. We replace the Lipschitz condition on the set-valued map in the right-hand side by a weaker one-sided Lipschitz (OSL), one-sided Kamke (OSK) or a continuity-like condition (CLC). We prove new(More)
In the paper we study weak and strong invariance of differential inclusions with fixed time impulses and with state constraints. We also investigate some properties of the solution set of impulsive system without state constraints. When the right-hand side is one sided Lipschitz we prove also the relaxation theorem and study the funnel equation of the(More)