Boundary Value Problems
Volume 2010 (2010), Article ID 106962, 9 pages
Research Article

Uniqueness and Parameter Dependence of Positive Solution of Fourth-Order Nonhomogeneous BVPs

Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China

Received 23 February 2010; Accepted 11 July 2010

Academic Editor: Irena Rachůnková

Copyright © 2010 Jian-Ping Sun and Xiao-Yun Wang. 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 following fourth-order four-point nonhomogeneous Sturm-Liouville boundary value problem: u(4)=f(t,u),t[0,1], αu(0)βu(0)=λ1,γu(1)+δu(1)=λ2, au′′(ξ1)bu′′′(ξ1)=λ3,cu′′(ξ2)+du′′′(ξ2)=λ4, where 0ξ1<ξ21 and λi(i=1,2,3,4) are nonnegative parameters. Some sufficient conditions are given for the existence and uniqueness of a positive solution. The dependence of the solution on the parameters λi(i=1,2,3,4) is also studied.