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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
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References:
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