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On regularization of right hand sides of differential relations. (English) Zbl 0561.34044

Let the values of F be convex compact subsets of \(R^ n\) and let F be upper semicontinuous with respect to x. There are two ways known of replacing F by a more regular map so that the set of solutions of \(\dot x\in F(t,x)\) remains unchanged. We prove that both ways lead to the same more regular map and extend the results to the case where \(R^ n\) is replaced by a separable Banach space.

MSC:

34G10 Linear differential equations in abstract spaces
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