Sweeping process with unbounded nonconvex perturbation

Abstract

A convex sweeping process with unbounded nonconvex perturbation term of a rather general form is investigated in a separable Hilbert space. We consider our sweeping process as an evolution inclusion with subdifferential operators. This allows to prove the theorem on existence of solutions under conditions generalizing the usual assumptions for convex sweeping processes. In particular, we show that multivalued mappings whose values are hyperplanes, half-spaces, etc. may be chosen as multivalued mappings generating the sweeping process. Such mappings do not satisfy the conditions under which convex sweeping processes are usually studied.