Abstract
Recently, a great advance has been made in the study of sweeping process variational inequalities with the papers (Chemetov, Monteiro Marques Set-Valued Anal. 15, 209–221, 2007 Castaing et al. J. Nonlinear Convex Anal. 10, 1–20, 2009 Haddad J. Optim. Theory Appl. 159, 386–398, 2013 Azzam-Laouir et al. Set-Valued Var. Anal. 22, 271–283, 2014 where, for a prox-regular moving set depending on both the time and the state, several existence results are provided. Those authors also studied the case where such a differential inclusion is perturbed by multimapping. The present paper establishes the existence of solutions for such perturbed differential inclusions in some context not considered in the previous papers.