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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 519346, 9 pages
http://dx.doi.org/10.1155/2013/519346
Research Article

Positive Solutions for Resonant and Nonresonant Nonlinear Third-Order Multipoint Boundary Value Problems

Department of Mathematics, Hefei Normal University, Hefei, Anhui 230061, China

Received 5 December 2012; Accepted 24 January 2013

Academic Editor: Chuanzhi Bai

Copyright © 2013 Liu Yang et al. 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

Positive solutions for a kind of third-order multipoint boundary value problem under the nonresonant conditions and the resonant conditions are considered. In the nonresonant case, by using the Leggett-Williams fixed point theorem, the existence of at least three positive solutions is obtained. In the resonant case, by using the Leggett-Williams norm-type theorem due to O’Regan and Zima, the existence result of at least one positive solution is established. It is remarkable to point out that it is the first time that the positive solution is considered for the third-order boundary value problem at resonance. Some examples are given to demonstrate the main results of the paper.