Résumé:
In this dissertation, we study, on the one hand, the existence and uniqueness of solution for integro-differential inclusions of the Volterra type and, on the other hand, the existence of optimal solutions and then obtain necessary optimality conditions for a broad class of local minimizers in such problems. The first topic is devoted to Moreau’s sweeping processes per- turbed by a sum of a Carath´eodory mapping and an integral forcing term in infinite dimensional framework. The moving set is assumed to be prox-regular and moved in an absolutely variation way. Applications to the theory of complementarity problems, non regular electric circuits and evolution variational inequalities are given. In the other topic, we give necessary optimality conditions which are expressed entirely in terms of the problem data and are illustrated by nontrivial examples that include applications to optimal control models of non-regular electri- cal circuits.
