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Random coincidence degree theory with applications to random differential inclusions. (English) Zbl 0886.47030
Authors’ abstract: The aim of this paper is to establish a random coincidence degree theory. This degree theory possesses all the usual properties of the deterministic degree theory such as existence of solutions, excision and Borsuk’s odd mapping theorem. Our degree theory provides a method for proving the existence of random solutions of the equation $$Lx\in N(\omega, x)$$ where $$L\: \operatorname {dom} L\subset X\to Z$$ is a linear Fredholm mapping of index zero and $$N\: \Omega \times \overline G\to 2^Z$$ is a noncompact Carathéodory mapping. Applications to random differential inclusions are also considered.
Correction see ibid. 38, No. 4, 815 (1997).
Reviewer: J.Andres (Olomouc)

##### MSC:
 47H04 Set-valued operators 47H40 Random nonlinear operators
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