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.