Abstract
In this paper we consider a Cauchy problem in which is present an evolution inclusion driven by the Fréchet subdifferential o ∂−f of a function
f:Ω→R∪{+∞} (Ω is an open subset of a real separable Hilbert space)
having a φ-monotone . subdifferential of order two and a perturbation
F:I×Ω→Pfc(H) with nonempty, closed and convex values.
First we show that the Cauchy problem has a nonempty solution set
which is an Rδ-set in C(I,H), in particular, compact and acyclic. Moreover, we obtain a Kneser-type theorem. In addition, we establish a continuity result about the solution-multifunction x→S(x). We also produce a
continuous selector for the multifunction x→S(x). As an application of
this result, we obtain the existence of solutions for a periodic problem.