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Nonexistence of solutions for differential inclusions with upper semicontinuous nonconvex right-hand side. (English) Zbl 0662.34018
In this note the author considers the differential inclusion \((1)\quad \dot x(t)=f(x(t),u(t)),\) \(x(0)=0\in R^ n\), \((2)\quad u(t)\in R(x(t)),\) where \(f: R^ n\times R^ m\to R^ n\) is continuous and \(R: R^ n\to R^ m\) is an upper semicontinuous multifunction with compact convex values. The author gives two counterexamples showing that these conditions are not sufficient to ensure the existence property for (1), (2).
Reviewer: I.I.Vrabie

MSC:
34A60 Ordinary differential inclusions
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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References:
[1] J.P. Aubin - A. CELLINA, Differential Inclusions , Springer , Berlin , 1984 . MR 755330 | Zbl 0538.34007 · Zbl 0538.34007
[2] J.P. Aubin - H. FRANKOWSKA, Trajectories lourdes de systèmes contrôlés , C. R. Acad. Paris Sér. I Math. , 298 ( 1984 ), pp. 521 - 524 . MR 753904 | Zbl 0561.49011 · Zbl 0561.49011
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