Existence of a Mild Solution to a Second-Order Impulsive Functional-Differential Equation with a Nonlocal Condition

Abstract

An abstract second-order semilinear functional-differential equation such that the linear part of its right-hand side is given by the infinitesimal generator of a strongly continuous cosine family of bounded linear operators, and provided with impulse and nonlocal conditions is studied. Under not too restrictive conditions the existence of a mild solution is proved using Schauder’s fixed point theorem. 2010 Mathematics Subject Classification: 34A37, 34G20.