Generalized multipoint conjugate eigenvalue problems

This paper considers the following boundary value problem: y((n))(t) = lambda P(t, y), t is an element of (0, 1), y((j))(t(i)) = 0, j = 0,..., n(i)-1, i = 1,..., r, where r greater than or equal to 2, n(i) greater than or equal to 1 for i = 1,..., r, Sigma(i=1)(r) n(i) = n and 0 = t(1) < t(2) < ... < t(r) = 1. We shall determine those positive values of lambda for which the boundary valu e problem has a solution that is "positive" in some sense. Specifically, cr iteria are developed for lambda to constitute an interval, bounded as well as unbounded, more so explicit intervals of lambda are presented. We also i nclude examples to illustrate the importance of the results obtained. (C) 2 000 Elsevier Science Ltd. All rights reserved.