Open Access

Eigenvalue comparisons for boundary value problems of the discrete beam equation

Advances in Difference Equations20062006:081025

DOI: 10.1155/ADE/2006/81025

Received: 29 September 2005

Accepted: 24 February 2006

Published: 24 July 2006

Abstract

We study the behavior of all eigenvalues for boundary value problems of fourth-order difference equations Δ4y i = λai+2yi+2, -1≤in-2, y0 = Δ2y-1 = Δy n = Δ3yn-1 = 0, as the sequence varies. A comparison theorem of all eigenvalues is established for two sequences and with a j b j , 1 ≤ jn, and the existence of positive eigenvector corresponding to the smallest eigenvalue of the problem is also obtained in this paper.

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Authors’ Affiliations

(1)
Department of Mathematics, Kennesaw State University

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Copyright

© Jun Ji and Yang 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.