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摘要
The aim of this paper is to establish the existence of anti-periodic solutions to the following nonlinear anti-periodic problem:. (x) over dot + A(t, x) is an element of Ext F(t, x) a.e. t is an element of I, x(T) = -x(0), in R-N where Ext F(t, x) denotes the extremal point set of the multifunction F(t, x), and A(t, x) is a nonlinear map from R-N to R-N. Sufficient conditions for the existence of extremal solutions are presented. Also, we prove that the extremal point set of this problem is compact in C(I, R-N) and dense in the solution set of nonlinear evolution problems with a convex valued perturbation which is multivalued. We apply our results on the control system with a priori feedback.
