Approximate controllability of some nonlinear systems in Banach spaces

In this paper, abstract results concerning the approximate controllability of semilinear evolution systems in a separable reflexive Banach space are obtained. Approximate controllability result for semilinear systems is obtained by means of Schauder's fixed-point theorem under the compactness assumption of the linear operator involved. It is also proven that the controllability of the linear system implies the controllability of the associated semilinear system. Then the obtained results are applied to derive sufficient conditions for the approximate controllability of the semilinear integrodifferential equations in Banach spaces and heat equations.