On nonlinear, nonconvex evolution inclusions

Abstract

We consider a nonlinear evolution inclusion driven by an m-accretive operator which generates an equicontinuous nonlinear semigroup of contractions. We establish the existence of extremal integral solutions and we show that they form a dense, G_δ-subset of the solution set of the original Cauchy problem. As an application, we obtain “bang-bang” type theorems for two nonlinear parabolic distributed parameter control systems.