Advances in Difference Equations
Volume 2006 (2006), Article ID 81025, 9 pages
Eigenvalue comparisons for boundary value problems of the discrete beam equation
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 , , , as the sequence varies. A comparison theorem of all
eigenvalues is established for two sequences and with , , and the existence of positive eigenvector corresponding to the
smallest eigenvalue of the problem is also obtained in this paper.