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

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

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.