## 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

### Keywords:

regularization of right hand sides
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### References:

 [1] Klee, Math. Scand. 20 pp 290– (1967) · Zbl 0162.44104 [2] Tolstonogov, Mat. Sb. 118 pp 3– (1982) [3] Tolstonogov, Sibirsk. Mat. Ž. 22 pp 182– (1981) [4] Jarník, Časopis Pěst. Mat. 102 pp 334– (1977) [5] Castaing, Lecture Notes in Mathematics 580 (1977) [6] Rzeźuchowski, Bull. Acad. Polon. Sci. Sér. Sci. Math. 28 pp 61– (1980) [7] Scorza-Dragoni, Rend. Sem. Mat. Padova 17 pp 102– (1948)
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