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

Tiziana Cardinali

International Journal of Stochastic Analysis, 2000, vol. 13, 1-22

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.

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:853782

DOI: 10.1155/S104895330000006X

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