arXiv subjects
Publications and source records attributed to Mikhail Krastanov.
A sufficient condition for existence of a solution of a differential inclusion with a uniformly bounded right-hand side that has nonempty closed (possibly nonconvex) values is obtained. An Olech-type result is obtained as a corollary. An example, which originates from the Fuller problem from optimal control theory, is given to demonstrate the applicability of the main result.
This is the first of two closely related papers on transversality. Here we introduce the notion of tangential transversality of two closed subsets of a Banach space. It is an intermediate property between transversality and subtransversality. Using it, we obtain a variety of known results and some new ones in a unified way. Our proofs do not use variational principles and we are concentrated mainly on tangential conditions in the primal space.
This is the second of two closely related papers on transversality. Here we introduce the notion of strong tangential transversality of two closed subsets of a Banach space which is a natural sufficient condition for tangential transversality. Some properties of uniform tangent sets are obtained. A new sum rule for the Clarke subdifferential is proven.
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.