This paper is devoted to the development of new sufficient conditions for the calmness and the Aubin property of implicit multifunctions. As the basic tool we employ the directional limiting coderivative which, together with the graphical derivative, enables a fine analysis of the local behavior of the investigated multifunction along relevant directions. For verification of the calmness proper...

We prove a Filippov type existence theorem for mild solutions of a nonconvex evolution inclusion by applying the contraction principle in the space of selections of the multifunction instead of the space of solutions.

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.