Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 154, pp. 1-9.
Title: Positive solutions for third-order Sturm-Liouville boundary-value
problems with p-Laplacian
Authors: Chengbo Zhai (Shanxi Univ., China)
Chunmei Guo (Shanxi Univ., China)
Abstract:
In this article, we consider the third-order Sturm-Liouville boundary
value problem, with $p$-Laplacian,
$$\displaylines{
(\phi_p(u''(t)))'+f(t,u(t))=0, \quad t\in (0,1),\cr
\alpha u(0)-\beta u'(0)=0,\quad \gamma u(1)+\delta u'(1)=0,\quad u''(0)=0,
}$$
where $\phi_p(s)=|s|^{p-2}s$, $p>1$.
By means of the Leggett-Williams fixed-point theorems, we prove
the existence of multiple positive solutions.
As an application, we give an example that illustrates our result.
Submitted September 1, 2008. Published November 28, 2009.
Math Subject Classifications: 34K10
Key Words: Positive solution; Sturm-Liouville
boundary value problem; p-Laplacian operator;
concave functional; fixed point.