Nonconvex Sweeping Process with Non-Compact Valued Perturbation and with Delay

The sweeping processes correspond to several important mechanical problems. Therefore, the existence theorems of solutions for sweeping processes have been attracted the attention by many authors. In this paper, we aim to prove existence theorems concerning the existence of solutions for functional differential inclusions governed by sweeping process with non- compact valued perturbations. Depending on a discretization technique used in recent papers, we prove two new existence results of solutions for first and second order functional differential inclusions governed by sweeping process with non- compact valued perturbations, where the moving set is a multifunction depending on time and state and with nonempty closed uniformly ρ-prox-regular values. We do not assume that the values of the moving set are contained in a fixed compact subset. In addition, our technique allows us to discuss some sweeping process problems with noncompact perturbations.