Approximate Controllability for Nonautonomous Integrodifferential Equations with State-dependent Delay

In this work, we study the existence of mild solutions and the approximate controllability for nonautonomous integrodifferential equations with state-dependent delay. We assume the approximate controllability of the linear part, then we use the resolvent operators theory to prove the approximate controllability of the nonlinear case. An example of one-dimensional heat equation with memory is given to illustrate our basic results.