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Approximate and relaxed solutions of differential inclusions. (English) Zbl 0688.34007
Let F be an upper semicontinuous multivalued map from $${\mathbb{R}}^{n+1}$$ into the compact subsets of $${\mathbb{R}}^ n$$. It is shown that x is a solution of the differential inclusion $$\dot x\in conv. hull F(t,x)$$ if and only if it is uniform limit of (suitably defined) approximate solutions in the sense of graph of the differential inclusion $$\dot x\in F(t,x)$$. This provides a generalization to upper semicontinuous differential inclusions of a result by T. Ważewski [Bull. Acad. Pol. Sci., Ser. Sci. Phys. Astron. 10, 11-15 (1962; Zbl 0104.304)].
Reviewer: G.Colombo

##### MSC:
 34A60 Ordinary differential inclusions
Full Text:
##### References:
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