On the structure of the solution set of evolution inclusions with Fréchet subdifferentials
Tiziana Cardinali · International Journal of Stochastic Analysis · 1999
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.