On the structure of the solution set of evolution inclusions with Fréchet subdifferentials
In this paper we consider a Cauchy problem in which is present an evolution inclusion driven by the Fréchet subdifferential o of a function ( is an open subset of a real separable Hilbert space) having a -monotone . subdifferential of order two and a perturbation with nonempty, closed and convex values.First we show that the Cauchy problem has a nonempty solution set which is an -set in , in particular, compact and acyclic. Moreover, we obtain a Kneser-type theorem. In addition, we establish a continuity result about the solution-multifunction . We also produce a continuous selector for the multifunction . As an application of this result, we obtain the existence of solutions for a periodic problem.