An existence result for a new variant of the nonconvex sweeping process

Abstract

In this paper we prove the existence of solutions of the following new variant of the nonconvex sweeping process with perturbation $-Au(t)\in N_{C(t)}(\dot{u}(t))+\ddot{u}(t)+F(t,\dot{u}(t))$ a.e. on $[0,T]$ ($T>0$).