Approximate controllability of retarded semilinear systems in Hilbert space

Abstract

In this paper, using Schauder's fixed point theorem, different sufficient conditions to the approximate controllability for a class of retarded semilinear control systems with bounded delay are established. The existence and uniqueness of mild solution is also proved. In particular, it is assumed that the nonlinear function is locally Lipschitz continuous and satisfies linear growth condition. This theory relax assumptions on nonlinear term of the semilinear system made by earlier authors. Finally, an example is given to show the application of our main result.