Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 147, pp. 1-29.

Title: Multiple positive solutions for singular m-point
       boundary-value problems with nonlinearities depending 
       on the derivative

Authors: Ya Ma        (Shandong Normal Univ., Jinan, China)
         Baoqiang Yan (Shandong Normal Univ., Jinan, China)

Abstract:
 Using the fixed point theorem in cones, this paper
 shows the existence of multiple positive solutions for the
 singular $m$-point boundary-value problem
 $$\displaylines{
 x''(t)+a(t)f(t,x(t),x'(t))=0,\quad 0<t<1,\cr
 x'(0)=0,\quad x(1)= \sum_{i=1}^{m-2}a_{i}x(\xi_i),
 }$$
 where $0<\xi_1<\xi_2<\dots<\xi_{m-2}<1$, $a_i\in [0,1)$,
 $i = 1, 2,\dots, m-2$, with $0< \sum_{i=1}^{m-2}a_i <1 $ and
 $f$  maybe singular at $x=0$ and $x'=0$.
  
Submitted August 13, 2008. Published October 24, 2008.
Math Subject Classifications: 34B10, 34B15.
Key Words: m-point boundary-value problem; singularity;
           positive solutions; fixed point theorem.