On the solution sets of nonconvex differential inclusions (Q1919800)

This paper is concerned with the solution set of the differential inclusion \(x'(t) \in \text{ext} F (t,x (t))\), where \(\text{ext} F\) denotes the set of extreme points of a set-valued map \(F\) with nonempty compact convex values. It was previously proved by the authors [Nonlinear Anal., Theory Methods Appl. 20, 871-894 (1993; Zbl 0774.34010)] that if in addition \(F\) is either Lipschitzian, or continuous with values that have nonempty interior, the solution set of the above differential inclusion is simply connected. The main result of the present paper states that under the same assumptions the solution set of the above differential inclusion is even contractible.