Existence Results for Second-Order Impulsive Neutral Functional Differential Equations with Nonlocal Conditions

The study of impulsive functional differential equations is linked to their utility in simulating processes and phenomena subject to short-time perturbations during their evolution. The perturbations are performed discretely and their duration is negligible in comparison with the total duration of the processes. That is why the perturbations are considered to take place “instantaneously” in the form of impulses. The theory of impulsive differential and functional differential equations has been extensively developed; see the monographs of Bainov and Simeonov 1 , Lakshmikantham et al. 2 , and Samoilenko and Perestyuk 3 , where numerous properties of their solutions are studied, and detailed bibliographies are given. This paper is devoted to extending existing results to second-order differential equations. To be precise, in 4 , the authors used Sadovsii’s fixed point theorem for a condensing map to establish existence results for first-order impulsive semilinear neutral functional differential inclusions with nonlocal conditions. Here, we obtain existence results for second-order semilinear impulsive differential equations with nonlocal conditions of the form