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

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.
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