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.