Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 1, Pages 51-72

On the structure of the solution set of evolution inclusions with Fréchet subdifferentials

Tiziana Cardinali

Perugia University, Department of Mathematics, Via Vanvitelli 1, Perugia 06123, Italy

Received 1 May 1998; Revised 1 November 1999

Copyright © 2000 Tiziana Cardinali. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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:ΩR{+} (Ω is an open subset of a real separable Hilbert space) having a φ-monotone . subdifferential of order two and a perturbation F:I×ΩPfc(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 xS(x). We also produce a continuous selector for the multifunction xS(x). As an application of this result, we obtain the existence of solutions for a periodic problem.