Copyright © 2012 Hairong Lian and Junfang Zhao. 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 generalize the unbounded upper and lower solution method
to a third-order ordinary differential equation on the half line subject to the Sturm-Liouville
boundary conditions. By using such techniques and the Schäuder fixed point theorem, some
criteria are presented for the existence of solutions and positive ones to the problem discussed.