Sweeping process with right uniformly lower semicontinuous mappings

Abstract

In this paper, we establish, in the setting of infinite dimensional Hilbert space, a new existence result for nonconvex sweeping process with right uniformly lower semicontinuous sets. This class of sets is more general than the classical assumption of absolutely continuous sets, and contains hyperplanes and half-spaces. Further, we apply on the problem an unbounded set-valued perturbation and we state the existence of solution.