Existence of multiple positive solutions for multipoint boundary value problems with a one-dimensional p-Laplacian

In this paper we consider the multipoint boundary value problem for a one-dimensional p-Laplacian: (phi(p) (u'))' + a(t) f (t, u) = 0, t is an element of (0, 1) u(0) = 0, u(1) = Sigma(m-2)(i=1) a(i)u(xi i), where phi(p)(s) = \s\(p-2)s, p > 1, 0 < xi(1) < xi(2) < ... <xi(m-2) < 1, a(i) >= 0, for i = 1, 2,..., m - 3 and a(m-2) > 0. Using a fixed point theorem for operators on a cone, we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem. (c) 2006 Elsevier Ltd. All rights reserved.