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On the existence of periodic solutions for nonconvex-valued differential inclusions in N . (English) Zbl 0851.34014
This paper deals with the multivalued periodic problem x ' F(t,x(t)), x(0)=x(b), where F:[0,b]× n n is a set-valued function with closed (not necessary convex 0) values, measurable with respect to both variables and lower semicontinuous with respect to the second variable. Using a tangential condition and directional selectors the authors establish the existence of periodic solutions. It is worth to note that on that occasion they prove a useful version of the Scorza-Dragoni property for lower semicontinuous multifunctions and they also study the lower semicontinuity of the intersection of two multifunctions.

34A60Differential inclusions
34C25Periodic solutions of ODE