ON THE STRUCTURE OF THE SOLUTION SET FOR DIFFERENTIAL INCLUSIONS IN A BANACH SPACE

In this article a differential inclusion is considered, where the mapping takes values in the family of all nonempty compact convex subsets of a Banach space, is upper semicontinuous with respect to for almost every , and has a strongly measurable selection for every . Under certain compactness conditions on 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.