Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 39, pp. 1-10.

Title: Positive solutions of singular fourth-order  boundary-value problems
       
Authors: Yujun Cui (Shandong  Univ. of Science, China)
         Yumei Zou (Shandong  Univ. of Science, China)

Abstract: 
 In this paper, we present necessary and sufficient conditions
 for the existence of  positive $C^3[0,1]\cap C^4(0,1)$ solutions
 for the singular boundary-value problem
 $$\displaylines{ 
 x''''(t)=p(t)f(x(t)),\quad t\in(0,1);\cr
 x(0)=x(1)=x'(0)=x'(1)=0,
 }$$
 where  $f(x)$ is either superlinear or sublinear,
 $p:(0,1)\to [0,+\infty)$ may be singular at both ends $t=0$
 and $t=1$.
 For this goal, we  use  fixed-point index results.
  
Submitted September 6, 2005. Published March 21, 2006
Math Subject Classifications: 34A34, 34B15, 45G15.
Key Words: Singular boundary value problem; fixed point theorem;
           positive solution.