Boundary Value Problems
Volume 2007 (2007), Article ID 68758, 10 pages
doi:10.1155/2007/68758
Research Article
Existence of Positive Solutions for Fourth-Order Three-Point Boundary Value Problems
Department of Mathematics, Huaiyin Teachers College, Huaian 223300, China
Received 11 July 2007; Accepted 7 November 2007
Academic Editor: Jean Mawhin
Copyright © 2007 Chuanzhi Bai. 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 nonlinear fourth-order three-point boundary value problem u(4)(t)=a(t)f(u(t)), 0<t<1, u(0)=u(1)=0, αu″(η)−βu‴(η)=0, γu″(1)+δu‴(1)=0. By using Krasnoselskii's fixed point theorem in a cone, we get some existence results of positive solutions.