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.

Abstract

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 0≤ξ1<ξ2≤1 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.