Solutions of constant signs of a system of Sturm-Liouville boundary value problems

We consider the following system u(i)((m)) (t) + f(i)(t, u(1), (t), u(2)(t),...,un(t)) + 0, t epsilon[0,1] u(i)((j)) (0) + 0, 0 less than or equal to j less than or equal to m - 3, alpha(i)u(i)((m - 2)) (0) - beta(i)u(i)((m - 1)) (0) = 0, gamma(i)u(i)((m - 2))(1) + delta(i)u(i)((m - 1)) (1) = 0, i = 1, 2,..., n, where m greater than or equal to 2 and for each 1 less than or equal to i less than or equal to n, beta(i) greater than or equal to 0, delta(i) greater than or equal to 0, beta(i) + alpha(i) > 0, delta(i) + gamma(i) > 0, and alpha(i)gamma(i) + alpha(i)delta(i) + beta(i)gamma(i) > 0. Criteria are offeres for the existence pf single and twin resolutions of the system that are of constant signs. (C) Elsevier Science Ltd. All rights reserved.