Continuous dependence results for a class of evolution inclusions

Abstract

In this paper we examine the dependence of the solutions of an evolution inclusion on a parameter λ We prove two dependence theorems. In the first the parameter appears only in the orientor field and we show that the solution set depends continuously on it for both the Vietoris and Hausdorff topologies. In the second the parameter appears also in the monotone operator. Using the notion of G-convergence of operators we prove that the solution set is upper semicontinuous with respect to the parameter. Both results make use of a general existence theorem which we also prove in this paper. Finally, we present two examples. One from control theory and the other from partial differential inclusions.