Eigenvalues of fourth-order singular Sturm-Liouville boundary value problems

In this paper, by establishing a new comparison theorem and constructing upper and lower solutions, some sufficient conditions of existence of positive solutions for the following nonlinear fourth-order singular Sturm-Liouville eigenvalue problem: [GRAPHICS] are established due to the Schauder's fixed point theorem for lambda large enough, where alpha, beta, gamma, delta >= 0 beta gamma + alpha gamma + alpha delta > 0, f and p can be singular at t = 0 and/or 1; moreover f can also be singular at u = 0. In addition, some peculiar cases are discussed and some further results are obtained. (c) 2006 Elsevier Ltd. All rights reserved.