Random differential inclusions depending on a parameter
type: Item
instance of: scholarly article
title: Random differential inclusions depending on a parameter
zbMATH Open document ID: 0749.60065
DOI: 10.1016/0022-247X(91)90360-C
author: Gabriele Bonanno
author: Salvatore A. Marano
published in: Journal of Mathematical Analysis and Applications
publication date: 1992-09-27T00:00:00Z
review text: The paper deals with the random multi-valued Cauchy problem \({d\over dt} x(\omega,t)\in F(\omega,t,x(\omega,t),\lambda)\), \(x(\omega,a)=\eta(\omega)\). Here \(F\) is a multifunction from \(\Omega\times[a,b]\times X\times\Lambda\) into \(X\), where \((\Omega,{\mathfrak F},\mu)\) is a complete probability space, \(X\) is a separable Banach space, \(\Lambda\) is a first countable topological space, and \(\eta\) is a measurable function from \(\Omega\) into \(X\). Let \(\Gamma(\eta,\lambda)\) be the set of all random solutions of the problem above. The main result, under suitable hypotheses, insures the lower semicontinuity of the multifunction \(\lambda\to\Gamma(\eta,\lambda)\). It extends to random differential inclusions a previous theorem by \textit{O. Naselli Ricceri} and \textit{B. Ricceri} [Bull. Pol. Acad. Sci., Math. 37, 7-12 (1989)] and improves a result by \textit{A. Nowak} [ibid. 34, 487-494 (1986; Zbl 0617.60059)]. A further result deals with the lipschitzianity of the multifunction \((\eta,\lambda)\to\Gamma(\eta,\lambda)\). It seems that this paper gives a contribution to random differential equations, along directions not previously studied.
Mathematics Subject Classification ID: 60H25
Mathematics Subject Classification ID: 49K24
Mathematics Subject Classification ID: 34A60
zbMATH DE Number: 57291
zbMATH Keywords: random multi-valued Cauchy problem
zbMATH Keywords: multifunction
zbMATH Keywords: lower semicontinuity
zbMATH Keywords: random differential inclusions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 57291