On the Structure of the Solution Set of Evolution Inclusions with Time{dependent Subdifferentials

In this paper we consider evolution inclusions driven by a time dependent subdifferential operator and a set-valued perturbation term. First we show that the problem with a convex-valued, h∗-u.s.c. orientor field (i.e. perturbation term) has a nonempty solution set which is an Rδ-set in C(T,H), in particular then compact and acyclic. For the non convex problem (i.e. the orientor field is non convex-valued), without assuming that the functional φ(t, x) of the subdifferential is of compact type, we show that for every initial datum ξ ∈ domφ(0, ·) the solution set S(ξ) is nonempty and we also produce a continuous selector for the multifunctions ξ → S(ξ). Some examples of distributed parameter systems are also included.