ON THE SOLUTION SETS OF FOUR-POINT BOUNDARY VALUE PROBLEMS FOR NONCONVEX DIFFERENTIAL INCLUSIONS

We consider the multivalued problem u(t) is an element of F(t, u(t), u(t)) under four boundary conditions u(0) = x(0), u(eta) = u(theta) = u( T) where 0 < eta < phi < T and for F is a multifunctions from [0, T] x R-n x R-n to the nonempty compact subsets of R-n not necessary convex. We give a lemma which is useful in the study of four boundary problems for the differential equations and the differential inclusions. Further we have results that improve earlier theorems.