We prove the existence of solutions of a differentialinclusion u'\in F(t,u) in a separable Banach space X with a moving constraint D(t). F is globally measurable, weakly upper semicontinuous with respect to u and takes convex, weakly compact values. D is upper semicontinuous from the left, and, for every r>0, the sets D(t)\cap rB are compact. F and D fulfil a well-known tangential condition, which is expressed by means of the Bouligand cone.
A Viability Result in the Upper Semicontinuous Case / Gavioli, Andrea. - In: JOURNAL OF CONVEX ANALYSIS. - ISSN 0944-6532. - STAMPA. - 5:(1998), pp. 381-395.
A Viability Result in the Upper Semicontinuous Case
GAVIOLI, Andrea
1998
Abstract
We prove the existence of solutions of a differentialinclusion u'\in F(t,u) in a separable Banach space X with a moving constraint D(t). F is globally measurable, weakly upper semicontinuous with respect to u and takes convex, weakly compact values. D is upper semicontinuous from the left, and, for every r>0, the sets D(t)\cap rB are compact. F and D fulfil a well-known tangential condition, which is expressed by means of the Bouligand cone.
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