Multiple positive solutions for nonlinear m-point boundary value problems

In this paper, we consider the existence and multiplicity of positive solutions for the m-boundary value problems {(p(t)u')' - q(t)u + f(t, u) = 0, 0 < t < 1, {au(0) - bp(0)u'(0) = Sigma(i=1)(m-2) alpha(i)u(xi(i)), {cu(1) + dp(1)u'(1) = Sigma(i=1)(m-2) beta(i)u(xi(i)), where P is an element of C([0, 1], (0, infinity)), q is an element of C([0, 1], (0, infinity)) a, b, c, d is an element of [0, infinity), xi(i) is an element of (0, 1), alpha(i), beta(i), is an element of [0, infinity) (for i is an element of {1, . . . , m - 2}) are given constants satisfying some suitable conditions. Our results extend some of the existing literature on two-point boundary value problem. Our proofs are based on fixed point theorem in cones. (C) 2002 Elsevier Inc. All rights reserved.