Existence of Solution for a Second-Order Neutral Differential Equation with State Dependent Delay and Non-instantaneous Impulses

In this paper existence of mild solution of a class of second order partial neutral differential e- quation with state dependent delay and non-instantaneous impulses is investigated. Hausdorff measure of noncompactness and Darbo Sadovskii fixed point theorem are used to prove the existence. Also, some re- strictive conditions such as the compactness assumption on the associated cosine or sine family of operators and the Lipschitz conditions on the nonlinear functions are replaced by simple and natural assumptions. In the last section we also study an example to illustrate the presented result.