Generalized multipoint conjugate Eigenvalue problems

Abstract

This paper considers the following boundary value problem: y((n))(t) = λP(t,y), t ε (0, 1), y((j)) (t(i)) = 0, j = 0,..., n(i) - 1, i = 1,..., r, where r ≥ 2, n(i) ≥ 1 for i = 1,..., r, Σ(i=1)/(Γ) n(i) = n and 0 = t1 < t2 < ··· < t(r) = 1. We shall determine those positive values of λ for which the boundary value problem has a solution that is 'positive' in some sense. Specially, criteria are developed for λ to constitute an interval, bounded as well as unbounded, more so explicit intervals of λ are presented. We also include examples to illustrate the importance of the results obtained. (C) 2000 Elsevier Science Ltd.