Boundary Value Problems 
Volume 2007 (2007), Article ID 41589, 13 pages
doi:10.1155/2007/41589
Research Article

Existence of Solutions for Second-Order Nonlinear Impulsive Differential Equations with Periodic Boundary Value Conditions

Chuanzhi Bai1 and Dandan Yang2

 1Department of Mathematics, Huaiyin Teachers College, Huaian, Jiangsu 223300, China
2Department of Mathematics, Yangzhou University, Yangzhou 225002, China
Received 12 February 2007; Revised 19 March 2007; Accepted 13 April 2007

Recommended by Kanishka Perera

Abstract

We are concerned with the nonlinear second-order impulsive periodic boundary value problem u''(t)=f(t,u(t),u'(t)), t∈[0,T]∖{t1}, u(t1+)=u(t1−)+I(u(t1)), u'(t1+) =u' (t1−)+J(u(t1)), u(0)=u(T), u'(0)=u'(T), new criteria are established based on Schaefer's fixed-point theorem.