International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 8, Pages 451-461

A second-order impulsive Cauchy problem

Eduardo Hernández Morales

Departamento de Matemática, Instituto de Ciências Matemáticas de São Carlos, Universidade de São Paulo, Caixa Postal 668, São Carlos 13560-970, São Paulo, Brazil

Received 11 April 2001; Revised 20 December 2001

Copyright © 2002 Eduardo Hernández Morales. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.