An Abstract Impulsive Second-Order Functional-Differential Cauchy Problem with Nonlocal Conditions

Abstract

The main concern of the paper is to prove the existence, uniqueness and continuous dependence of mild and classical solutions of a semilinear impulsive second-order functional-differential equation with nonlocal initial conditions. We consider the Cauchy problem in general Banach spaces, and apply the theory of strongly continuous cosine families of linear operators and the Banach fixed-point theorem.