Boundary Value Problems for Nonconvex Differential Inclusions

In this paper we consider multivalued boundary value problems of the Sturm-Liouville type. First we prove the existence of extremal trajectories and then we show that they are dense in the solution set of the original convex problem. We also prove an existence theorem when the orientor field is l.s.c. and nonconvex valued. Some feedback control systems are also considered.