Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 75, pp. 1-10.

Title: Three positive solutions for m-point boundary-value problems
 with one-dimensional p-Laplacian
       
Authors: Donglong Bai (Shijiazhuang Mechanical Engineering College, China)
         Hanying Feng (Shijiazhuang Mechanical Engineering College, China)

Abstract:
 In this article, we study the multipoint boundary  value
 problem  for the one-dimensional p-Laplacian
 $$
 (\phi_p(u'))'+ q(t)f(t,u(t),u'(t))=0,\quad t\in (0,1),
 $$
 subject to the boundary  conditions
 $$
 u(0)=\sum_{i=1}^{m-2} a_iu(\xi_i),\quad  u'(1)=\beta u'(0).
 $$
 Using a fixed point theorem due to Avery and Peterson, we provide
 sufficient conditions for the existence of at least three positive
 solutions to the above boundary value problem. The interesting point
 is that the nonlinear term f involves  the first
 derivative of the unknown function.

Submitted April 5, 2011. Published June 16, 2011.
Math Subject Classifications: 34B10, 34B15, 34B18.
Key Words: Multipoint boundary value problem; positive solution; 
           Avery-Peterson fixed point theorem; one-dimensional p-Laplacian.