Boundary Value Problems
Volume 2008 (2008), Article ID 723828, 14 pages
Research Article

Solvability for Two Classes of Higher-Order Multi-Point Boundary Value Problems at Resonance

Yunzhu Gao and Minghe Pei

Department of Mathematics, Beihua University, Jilin City 132013, China

Received 13 July 2007; Revised 14 December 2007; Accepted 29 January 2008

Academic Editor: Ivan Kiguradze

Copyright © 2008 Yunzhu Gao and Minghe Pei. 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.


Using the theory of coincidence degree, we establish existence results of positive solutions for higher-order multi-point boundary value problems at resonance for ordinary differential equation u(n)(t)=f(t,u(t),u(t),,u(n1)(t))+e(t), t(0,1), with one of the following boundary conditions: u(i)(0)=0, i=1,2,, n2, u(n1)(0)=u(n1)(ξ), u(n2)(1)=j=1m2βju(n2)(ηj), and u(i)(0)=0, i=1,2,, n1, u(n2)(1)=j=1m2βju(n2)(ηj), where f:[0,1]×n=(,+) is a continuous function, e(t)L1[0,1]βj(1jm2,m4), 0<η1<η2<<ηm2<1, 0<ξ<1, all the βjs have not the same sign. We also give some examples to demonstrate our results.