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Journal of Mathematics
Volume 2014 (2014), Article ID 951947, 5 pages
http://dx.doi.org/10.1155/2014/951947
Research Article

Existence of Positive Solutions for Nonlinear Third-Order Boundary Value Problem

Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Received 13 May 2014; Accepted 8 October 2014; Published 19 October 2014

Academic Editor: Georgios Psihoyios

Copyright © 2014 Tiaoxia Dun and Pengyu Chen. 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 are concerned with the existence of positive solutions for the nonlinear third-order three-point boundary value problem , , , , where , , is a positive parameter, is continuous. We construct Green’s function for the associated linear boundary value problem and obtain some useful properties of Green’s function. Finally, by using fixed-point index theorem in cones, we establish the existence results of positive solutions for the boundary value problem an example illustrates the application of the results obtained.