International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 2000 / Article

Open Access

Volume 13 |Article ID 853782 | 22 pages | https://doi.org/10.1155/S104895330000006X

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

Received01 May 1998
Revised01 Nov 1999

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: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.

Copyright © 2000 Hindawi Publishing Corporation. 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.

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