Approximate controllability of impulsive system involving state-dependent delay and variable delay in control via fundamental solution

Abstract

This article is concerns with approximate controllability for a new class of impulsive semilinear control systems involving state-dependent delay and variable delay in control in Hilbert space setting. We formulate some new sufficient conditions which guarantee the existence of solution  to the considered system. We use the theory of fundamental solution and Krasnoselskii fixed point theorem to establish our major results. Finally, an example is constructed that demonstrate the effectiveness of obtained results.