Existence Results for First and Second Order Nonconvex Sweeping

Abstract. We are interested in existence results for nonconvex functional differential inclusions. First, we prove an existence result, in separable Hilbert spaces, for first order nonconvex sweeping processes with perturba-tion and with delay. Then, by using this result and a fixed point theorem we prove an existence result for second order nonconvex sweeping processes with perturbation and with delay of the form u̇(t) ∈ C(u(t)), ü(t) ∈ −NP (C(u(t)); u̇(t)) + F (t, u̇t) when C is a nonconvex bounded Lipschitz set-valued map-ping and F is a set-valued mapping with convex compact values taking their values in finite dimensional spaces