Journal of Applied Mathematics
Volume 2013 (2013), Article ID 721909, 6 pages
http://dx.doi.org/10.1155/2013/721909
Research Article

Positive Solutions for Third-Order Boundary-Value Problems with the Integral Boundary Conditions and Dependence on the First-Order Derivatives

Yanping Guo1 and Fei Yang2

1School of Electrical Engineering, Hebei University of Science and Technology, Shijiazhuang, Hebei 050018, China
2Nanchang Institute of Science and Technology, Nanchang, Jiangxi 330108, China

Received 8 April 2013; Revised 2 June 2013; Accepted 9 June 2013

Academic Editor: Wei-Shih Du

Copyright © 2013 Yanping Guo and Fei Yang. 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

By using a fixed point theorem in a cone and the nonlocal third-order BVP's Green function, the existence of at least one positive solution for the third-order boundary-value problem with the integral boundary conditions , , , , and is considered, where is a nonnegative continuous function, , and The emphasis here is that depends on the first-order derivatives.