Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 18, pp. 1-16.

Title: Positive and monotone solutions of an m-point boundary-value problem 
   
Author: Panos K. Palamides (Naval Academy of Greece)

Abstract: 
  We study the second-order ordinary differential equation 
  $$  y''(t)=-f(t,y(t),y'(t)),\quad 0\leq t\leq 1,  $$
  subject to the multi-point boundary conditions 
  $$
  \alpha y(0)\pm \beta y'(0)=0,\quad y(1)=\sum_{i=1}^{m-2}\alpha_iy(\xi_i)\,.
  $$
  We prove the existence of a positive solution (and monotone in some cases)
  under superlinear and/or sublinear growth rate in $f$. Our approach is based
  on an analysis of the corresponding vector field on the $(y,y')$
  face-plane and on Kneser's property for the solution's funnel.
 
Submitted January 10, 2002. Published February 18, 2002.
Math Subject Classifications: 34B10, 34B18, 34B15.
Key Words: multipoint boundary value problems; positive monotone
           solution; vector field; sublinear; superlinear; 
           Kneser's property; solution's funel.