No abstract

In this paper we prove, in a separable reflexive uniformly smooth Banach space, the existence of solutions of a perturbed first order differential inclusion governed by the proximal normal cone to a moving set depending on the time and on the state. The perturbation is assumed to be separately upper semicontinuous. Recently, the differential inclusion (1), where the sets in the normal cone depend on the time and the state, has been studied by many authors motivated by the applications of this type of sweeping processes to parabolic quasi variational inequalities and modelisation of 2D and 3D quasistatic evolution problems with