Abstract

We study the existence of mild and classical solutions for an abstract second-order impulsive Cauchy problem modeled in the form u¨(t)=Au(t)+f(t,u(t),u˙(t)),t(T0,T1),tti;u(0)=x0,u˙(0)=y0;u(ti)=Ii1(u(ti)).u˙(ti)=Ii2(u˙(ti+)) where A is the infinitesimal generator of a strongly continuous cosine family of linear operators on a Banach space X and f,Ii1, Ii2 are appropriate continuous functions.