On~the structure of the solution set for differential inclusions in a~Banach space

A. A. Tolstonogov

Sbornik. Mathematics, Tome 46 (1983) no. 1, pp. 1-15

Résumé

In this article a differential inclusion $\dot x\in\Gamma(t,x)$ is considered, where the mapping $\Gamma$ takes values in the family of all nonempty compact convex subsets of a Banach space, is upper semicontinuous with respect to $x$ for almost every $t$, and has a strongly measurable selection for every $x$. Under certain compactness conditions on $\Gamma$ proofs are given for a theorem on the existence of solutions, a theorem on the upper semicontinuous dependence of solutions on the initial conditions, and an analogue of the Kneser–Hukuhara theorem on connectedness of the solution set. Bibliography: 20 titles.