Abstract

We prove the existence of solutions of a differential inclusion u′ ∈ F(t, u) in a separable Banach space X with constraint u(t) ∈ 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) ∩ r B are compact. F and D fulfil a well-known tangential condition, which is expressed by means of the Bouligand cone.

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Andrea Gavioli

Dipartimento di Matematica Pura ed Applicata, Università di Modena, Via G. Campi 213/B, 41100 Modena, Italy

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Suggested citation

A. Gavioli. “A Viability Result in the Upper Semicontinuous Case.” Journal of Convex Analysis 5 (1998), No. 2, 381–395. https://doi.org/10.68381/jca05-24

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Published by Heldermann Verlag, 1998. Rights now held by Banach Press LLC.