Approximate controllability of damped second-order neutral differential equations with state-dependent delay

This article discusses the approximate controllability of damped second-order neutral differential equations with state-dependent delay. The results are obtained using strongly continuous cosine family theories and fixed-point theories. Assuming approximate controllability of the corresponding equation, we obtain sufficient conditions for approximate controllability of the nonlinear second-order equations. An application are provided to demonstrate how the proposed result can be applied.