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Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 357697, 14 pages
http://dx.doi.org/10.1155/2012/357697
Research Article

Existence of Unbounded Solutions for a Third-Order Boundary Value Problem on Infinite Intervals

School of Sciences, China University of Geosciences, Beijing 100083, China

Received 20 June 2012; Accepted 31 July 2012

Academic Editor: Zengji Du

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.

Abstract

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.