Boundary Value Problems
Volume 2011 (2011), Article ID 901796, 18 pages
doi:10.1155/2011/901796
Research Article

Existence Results of Three-Point Boundary Value Problems for Second-order Ordinary Differential Equations

Sheng-Ping Wang1 and Long-Yi Tsai2

1Holistic Education Center, Cardinal Tien College of Healthcare and Management, No.11, Zhongxing Road, Sanxing Township, Yilan County 26646, Taiwan
2Department of Mathematical Sciences, National ChengChi University, Taipei 11605, Taiwan

Received 19 May 2010; Revised 15 September 2010; Accepted 24 September 2010

Academic Editor: Daniel Franco

Copyright © 2011 Sheng-Ping Wang and Long-Yi Tsai. 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 establish existence results of the following three-point boundary value problems: u′′(t)+f(t,u(t))=0, t∈(0,1), (BC)u(0)=0 and u(1)=δu(η), where 0<η<1 and 0<δ≤1. The approach applied in this paper is upper and lower solution method associated with basic degree theory or Schauder's fixed point theorem. We deal with this problem with the function f which is Carathéodory or singular on its domain.