Positive solutions for eigenvalue problems of fourth-order elastic beam equations

摘要

In this paper, we investigate the positive solutions of equations omega((4))(t) = gimelf(t,omega(t)) with omega(0) = omega(1) = omega'(0) = omega'(1) = 0. We obtain several existence and multiplicity results by an application of the Krasnosel'skii fixed-point theorem of cone expansion-compression type. This class of equations usually describes the deformations of elastic beams with fixed both endpoints. (C) 2004 Elsevier Ltd. All rights reserved. [References: 6]