On the structure of the solution set of evolution inclusions with Fréchet subdifferentials. (2000) - Cardinali, Tiziana
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 → P f c ( H ) with nonempty, closed and convex values. First we show that the Cauchy problem has a nonempty solution set which is an R δ -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.