Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 84, pp. 1-6.

Title: Uniqueness and parameter dependence of solutions
       of fourth-order four-point nonhomogeneous BVPs

Authors: Jian-Ping Sun (Lanzhou Univ. of Tech., Lanzhou, China)
         Xiao-Yun Wang (Lanzhou Univ. of Tech., Lanzhou, China)

Abstract:
 In this article, we investigate the fourth-order
 four-point nonhomogeneous Sturm-Liouville boundary-value
 problem
 $$\displaylines{
 u^{(4)}(t)=f(t,u(t)),\quad t\in [0,1],  \cr
 \alpha u(0)-\beta u'(0)=\gamma u(1)+\delta u'(1)=0,  \cr
 au''(\xi _1)-bu'''(\xi _1)=-\lambda ,\quad
 cu''(\xi _2)+du'''(\xi _2)=-\mu ,
 }$$
 where $0\leq \xi _1<\xi _2\leq 1$ and $\lambda$ and $\mu $ are
 nonnegative parameters. We obtain sufficient conditions for
 the existence and uniqueness of positive solutions.
 The dependence of the solution on the parameters $\lambda$
 and $\mu$ is also studied.

Submitted September 21, 2009. Published June 18, 2010.
Math Subject Classifications: 34B08, 34B10.
Key Words: Nonhomogeneous; fourth-order; four-point; Sturm-Liouville;
           boundary-value problem; positive solution;
           uniqueness; dependence on parameter