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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 687595, 12 pages
Research Article

On the Existence of Positive Solutions of Resonant and Nonresonant Multipoint Boundary Value Problems for Third-Order Nonlinear Differential Equations

1Department of Mathematics, Hefei Normal University, Hefei, Anhui Province 230601, China
2College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Received 31 July 2013; Accepted 8 October 2013

Academic Editor: Zhanbing 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.


Positive solutions for a kind of third-order multipoint boundary value problem under the non-resonant conditions and the resonant conditions are considered. In the nonresonant case, by using Leggett-Williams fixed-point theorem, the existence of at least three positive solutions is obtained. In the resonant case, by using Leggett-Williams norm-type theorem due to O’Regan and Zima, existence result of at least one positive solution is established. The results obtained are valid and new for the problem discussed. Two examples are given to illustrate the main results.