International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 62512, 11 pages
doi:10.1155/IJMMS/2006/62512

On a class of second-order impulsive boundary value problem at resonance

Guolan Cai,1 Zengji Du,2 and Weigao Ge2

1Department of Mathematics and Computer, Central University for Nationalities, Beijing 100081, China
2Department of Applied Mathematics, Beijing Institute of Technology, Beijing 100081, China

Received 16 September 2004; Revised 4 December 2005; Accepted 18 December 2005

Copyright © 2006 Guolan Cai et al. 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.

Abstract

We consider the following impulsive boundary value problem, x″(t)=f(t,x,x′), t∈J\{t1,t2,…,tk}, Δx(ti)=Ii(x(ti),x′(ti)), Δx′(ti)=Ji(x(ti),x′(ti)), i=1,2,…,k, x(0)=(0), x′(1)=∑j=1m−2αjx′(ηj). By using the coincidence degree theory, a general theorem concerning the problem is given. Moreover, we get a concrete existence result which can be applied more conveniently than recent results. Our results extend some work concerning the usual m-point boundary value problem at resonance without impulses.