Boundary Value Problems
Volume 2010 (2010), Article ID 708376, 13 pages
doi:10.1155/2010/708376
Research Article

Multiple Positive Solutions for nth Order Multipoint Boundary Value Problem

Yaohong Li1,2 and Zhongli Wei2,3

1Department of Mathematics, Suzhou University, Suzhou, Anhui 234000, China
2School of Mathematics, Shandong University, Jinan, Shandong 250100, China
3School of Sciences, Shandong Jianzhu University, Jinan, Shandong 250101, China

Received 22 January 2010; Revised 9 April 2010; Accepted 3 June 2010

Academic Editor: Ivan T. Kiguradze

Copyright © 2010 Yaohong Li and Zhongli Wei. 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 study the existence of multiple positive solutions for nth-order multipoint boundary value problem. u(n)(t)+a(t)f(u(t))=0, t∈(0,1), u(j-1)(0)=0(j=1,2,…,n-1), u(1)=∑i=1mαiu(ηi), where n≥2, 0<η1<η2<⋯<ηm<1, αi>0,i=1,2,…,m. We obtained the existence of multiple positive solutions by applying the fixed point theorems of cone expansion and compression of norm type and Leggett-Williams fixed-point theorem. The results obtained in this paper are different from those in the literature.