Existence results for n-point boundary value problem of second order ordinary differential equations

This study concerns the existence of positive solutions to the boundary value problem u" + a(t) f(u) = 0, t is an element of (0, 1), u'(0) = Sigma(i=1)(n-2) b(i)u' (xi(i)), u(1) = Sigma(i=1)(n-2) a(i)u(xi(i)), where xi(i) is an element of (0, 1) with 0 < xi(1) < xi(2) < (...) < xi(n-2) < 1, a(i), b(i) is an element of [0, infinity) with 0 < Sigma(i=1)(n-2) a(i) < 1 and Sigma(i=1)(n-2) b(i) < 1. By applying the Krasnoselskii's fixed-point theorem in Banach spaces, some sufficient conditions guaranteeing the existence of at least one positive solution or at least two positive solutions are established for the above general n-point boundary value problem. (c) 2004 Elsevier B.V. All rights reserved.