Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 937670, 12 pages
Research Article

Positive Solutions for a Class of Third-Order Three-Point Boundary Value Problem

School of Mathematical Sciences, Jiangsu Normal University, Xuzhou, Jiangsu 221116, China

Received 25 November 2011; Accepted 8 February 2012

Academic Editor: Yong Zhou

Copyright © 2012 Xiaojie Lin and Zhengmin Fu. 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.


We investigate the problem of existence of positive solutions for the nonlinear third-order three-point boundary value problem u(t)+λa(t)f(u(t))=0, 0<t<1, u(0)=u(0)=0, u(1)=u(η), where λ is a positive parameter, (0,1), η(0,1), f:(0,)(0,), a:(0,1)(0,) are continuous. Using a specially constructed cone, the fixed point index theorems and Leray-Schauder degree, this work shows the existence and multiplicities of positive solutions for the nonlinear third-order boundary value problem. Some examples are given to demonstrate the main results.