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

Abstract

This article is concerned with the approximate controllability for a new class of impulsive semilinear control systems involving state-dependent delay and variable delay in control in Hilbert spaces. We formulate new sufficient conditions which guarantee the existence of solution to the considered system. We use the theory of fundamental solution, Krasnoselskii?s and Schauder?s fixed point theorems to establish our major results. Finally, two examples are constructed which demonstrate the effectiveness of obtained results.