Positive solutions of a nonlinear m-point boundary value problem

Let a(i) greater than or equal to 0 for i = 1, ..., m-3 and a(m-2) > 0. Let xi (i) satisfy 0 < xi (1) < xi (2) < ... < xi (m-2) < 1 and Sigma (m-2)(i= 1) a(i)xi (i) < 1. We study the existence of positive solutions to the boun dary-value problem u " + a(t)f(u) = 0, t is an element of (0,1), u(0) = 0, u(1) = where a is an element of C([0,1], [0,infinity)), and f is an element of C([0,infinity), [0,infinity)). We show the existence of at le ast one positive solution if f is either superlinear or sublinear by applyi ng a fixed-point theorem in cones. (C) 2001 Elsevier Science Ltd. All right s reserved.Sigma (m-2)(i=1) a(i)u(xi (i)),