Existence of three positive solutions for m-point boundary-value problems with one-dimensional p-Laplacian

In this paper, we consider the multipoint boundary value problem for the one-dimensional p-Laplacian (phi(p)(u'))' + q(t) f (t, u(t), u'(t)) = 0, t epsilon (0, 1), subject to the boundary conditions: u(0) = 0, u(1) = Sigma(m-2)(i=1) a(i)u(xi(i)), where phi(p)(s) = vertical bar s vertical bar(p-2)s, p > 1,xi(i) epsilon (0, 1) with 0 < xi(1) < xi(2) <... < xi(m-2) 1 and a(i) epsilon [0, 1), 0 <= Sigma(m-2)(i=1) a(i) < 1. Using a fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions to the above boundary value problem. The interesting point is that the nonlinear term f explicitly involves a first-order derivative. (c) 2007 Elsevier Ltd. All rights reserved.