Boundary Value Problems
Volume 2010 (2010), Article ID 519210, 11 pages
doi:10.1155/2010/519210
Research Article

Positive Solutions of a Nonlinear Three-Point Integral Boundary Value Problem

Jessada Tariboon1,2 and Thanin Sitthiwirattham1

1Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand
2Centre of Excellence in Mathematics, CHE, Sri Ayutthaya Road, Bangkok 10400, Thailand

Received 4 August 2010; Accepted 18 September 2010

Academic Editor: Raul F. Manasevich

Copyright © 2010 Jessada Tariboon and Thanin Sitthiwirattham. 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 positive solutions to the three-point integral boundary value problem u′′+a(t)f(u)=0, t∈(0,1), u(0)=0, α∫0ηu(s)ds=u(1), where 0<η<1 and 0<α<2/η2. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem in cones.