We prove the Lipschitz dependence on the initial condition of the solution set of a nonconvex second-order differential inclusions by applying the contraction principle in the space of selections of the multifunction instead of the space of solutions.

In this paper, we study continuity properties in Hausdorff topology for different special set multifunctions. Key–words: set multifunction, multi(sub)measure, regular, exhaustive, increasing/decreasing convergent, order continuity, probability.

The purpose of this paper is to introduce and study a new generalization of ω-continuous multifunction called slightly ω-continuous multifunctions in topological spaces. AMS (MOS) Subject Classification Codes: 54C10, 54C08, 54C05

In this paper we consider the Minimum Time Problem with dynamics given by a differential inclusion. We prove that the minimum time function is semiconcave under suitable hypotheses on the multifunction F.