Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 45, pp. 1-12.

Title: Multiple positive solutions for nonlinear second-order m-point
       boundary-value problems with sign changing nonlinearities
 
Authors: Fuyi Xu     (Shandong  Univ. of Technology, China)
         Zhenbo Chen (Shandong  Univ. of Technology, China)
	 Feng Xu     (Shandong  Univ. of Technology, China)

Abstract: 
 In this paper, we study the nonlinear second-order m-point
 boundary value problem
 $$\displaylines{
 u''(t)+f(t,u)=0,\quad  0\leq t \leq 1, \cr
 \beta u(0)-\gamma u'(0)=0,\quad
 u(1)=\sum _{i=1}^{m-2}\alpha_{i} u(\xi_{i}),
 }$$
 where the nonlinear term $f$ is allowed to change sign.
 We impose growth conditions  on $f$ which yield the existence of at
 least two  positive solutions by using  a  fixed-point theorem
 in double cones. Moreover, the associated Green's function for
 the above problem is given.
 
Submitted December 27, 2007. Published March 29, 2008.
Math Subject Classifications: 34B15.
Key Words: m-point;  boundary-value problem; Green's function;
           fixed point theorem in double cones.