A multivalued history-dependent operator and implicit evolution inclusions. II

Continuing the first part of this work, we study an implicit evolution inclusion with time-dependent maximal monotone operator in a separable Hilbert space. This inclusion involves some perturbation given by a multivalued history-dependent operator. We establish the existence of a solution. The solution is unique provided that the values of the multivalued history-dependent operator are singletons. We derive an explicit evolution inclusion resolved for the derivative with the same solution set. The results are applied to the implicit sweeping process generated by a moving closed convex set. All results are new since the implicit evolution inclusions with maximal monotone operators of general form have not been studied yet. The perturbing multivalued history-dependent operator, addressed in the first part, adds novelty too. As for the implicit sweeping processes, the main available results are particular cases of ours.