Advances in Difference Equations
Volume 2006 (2006), Article ID 81025, 9 pages

Eigenvalue comparisons for boundary value problems of the discrete beam equation

Jun Ji and Bo Yang

Department of Mathematics, Kennesaw State University, Kennesaw 30144, GA, USA

Received 29 September 2005; Revised 10 February 2006; Accepted 24 February 2006

Copyright © 2006 Jun Ji and Bo Yang. 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.


We study the behavior of all eigenvalues for boundary value problems of fourth-order difference equations Δ4yi=λai+2yi+2, 1in2, y0=Δ2y1=Δyn=Δ3yn1=0, as the sequence {ai}i=1n varies. A comparison theorem of all eigenvalues is established for two sequences {ai}i=1n and {bi}i=1n with ajbj, 1jn, and the existence of positive eigenvector corresponding to the smallest eigenvalue of the problem is also obtained in this paper.