Discussiones Mathematicae Differential Inclusions 15(2) (1995) 191-200

[BIBTex]

SET-VALUED RANDOM DIFFERENTIAL EQUATIONS IN BANACH SPACE

Mariusz Michta

Institute of Mathematics, Technical University
Podgórna 50, 65-246 Zielona Góra, Poland

Abstract

We consider the problem of the existence of solutions of the random set-valued equation:

(I)
DHXt = F(t,Xt)
P.1, t ∈ [0,T] -a.e.
X0 = U

P.1

where F and U are given random set-valued mappings with values in the space Kc(E), of all nonempty, compact and convex subsets of the separable Banach space E. Under certain restrictions on F we obtain existence of solutions of the problem (I). The connections between solutions of (I) and solutions of random differential inclusions are investigated.

Keywords: set-valued mappings, Hukuchara's derivative, Aumann's integral, measurability of multifunctions, measurable selectors.

1991 Mathematics Subject Classification: 26E25, 28B20.

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