Multiple symmetric positive solutions to a new kind of four point boundary value problem

In this paper, we are concerned with the existence of multiple symmetric positive solutions for four point boundary value problems with one-dimensional p-Laplacian (phi(p)(x'(t)))'+h(t)f (t,x(t),x'(t)) = 0. 0 < t < 1. subject to one of the following boundary conditions: x(0)+delta x'(xi) = 0, x(1) - delta x'(eta) = 0, or x(0)+g(x'(xi)) = 0, x(1) - g(x'(n)) = 0 where phi(p)(s) = vertical bar s vertical bar(p-2)s, p>1,xi+n =1. By using a fixed point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of at least three positive solutions. The interesting points here are that xi>eta and the nonlinear term f are involved with the first-order derivative explicitly. (c) 2008 Elsevier Ltd. All rights reserved.