Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 96, pp. 1-52.

Title: Solutions to second order non-homogeneous multi-point BVPs
       using a fixed-point theorem
  
Author: Yuji Liu (Guangdong Univ., Guangzhou, China)
 
Abstract: 
  In this article, we study five non-homogeneous multi-point
  boundary-value problems (BVPs) of second order differential
  equations with the one-dimensional p-Laplacian.
  These problems have a common equation (in different function domains)
  and different boundary conditions. We find conditions that
  guarantee the existence of at least three positive solutions.
  The results obtained  generalize several known ones and are illustrated
  by examples.
  It is also shown that the approach for getting three positive solutions
  by using multi-fixed-point theorems can be extended to
  nonhomogeneous BVPs.   The emphasis is on the nonhomogeneous
  boundary conditions and the nonlinear term involving first order
  derivative of the unknown. Some open problems are also proposed.
 
Submitted March 3, 2008. Published July 25, 2008.
Math Subject Classifications: 34B10, 34B15, 35B10.
Key Words: Second order; p-Laplacian; positive solution;
           mixed type multi-point boundary-value problem.