On the structure of the solution set of evolution inclusions with Fréchet subdifferentials. (2000)

• Record Type: Journal Article
• Authors: Cardinali, Tiziana
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 13:Number 1(2000)
• Page Start: 51
• Page End: 72
• Publication Date: 2000
• Subjects: upper semicontinuity -- Hausdorff metric -- Fréchet subdifferential -- evolution inclusion -- φ-monotone subdifferential of order two -- Rδ-set -- continuous selector -- periodic problem; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S104895330000006X
• Languages: English
• ISSNs: 1048-9533

Abstract

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.