Existence Results on the Second-Order Nonconvex Sweeping Processes with Perturbations

We prove several existence theorems for second-order differential inclusions of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\dot x(t) \in K(x(t)),\ddot x(t) \in - N(K(x(t));\dot x(t)) + F(t,x(t),\dot x(t))$$ \end{document}, when K and F are two convex or nonconvex set-valued mappings taking their values in a Hilbert space.