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Random functional-differential inclusions with nonconvex right hand side in a Banach space. (English) Zbl 0636.60066

Summary: We prove the existence of random solutions for stochastic functional- differential inclusions defined in a separable Banach space and with an orientor field which is nonconvex valued, lower semicontinuous and satisfies a compactness type hypothesis involving the Hausdorff measure of noncompactness.
The proof is based on the “measurable selection method” which makes use of an earlier deterministic result that we proved (to appear in Funkc. Ekvacioj). Our theorem extends the earlier results by Deimling, Ito, Ladde-Lakshmikantham and Nowak.

MSC:

60H25 Random operators and equations (aspects of stochastic analysis)
34G20 Nonlinear differential equations in abstract spaces
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