Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 116, pp. 1-20.

Title: Positive solutions for singular three-point 
       boundary-value problems
  
Authors: Ravi P. Agarwal (Florida Institute of Technology, USA)
         Donal O'Regan   (National Univ. Ireland, Galway, Ireland)
	 Baoqiang Yan    (Shandong Normal Univ., Ji-nan, China)
 
Abstract:
 Using the theory of fixed point index, this paper discusses the
 existence of at least one positive solution and the existence
 of multiple positive solutions for the singular three-point
 boundary value problem:
 $$\displaylines{
 y''(t)+a(t)f(t,y(t),y'(t))=0,\quad 0<t<1,\cr
 y'(0)=0,\quad y(1)=\alpha y(\eta),
 }$$
 where $0<\alpha<1$, $0<\eta<1$, and $f$ may be singular at 
 $y=0$ and $y'=0$.
 
Submitted January 17, 2008. Published August 25, 2008.
Math Subject Classifications: 34B15.
Key Words: Three-point boundary value problems; singularity;
           positive solutions; fixed point index.