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