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.
We establish existence results of the following three-point boundary value problems: , , and , where and . 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 which is Carathéodory or singular on its domain.