Advances in Difference Equations
Volume 2006 (2006), Article ID 81025, 9 pages
doi:10.1155/ADE/2006/81025

Eigenvalue comparisons for boundary value problems of the discrete beam equation

Abstract

We study the behavior of all eigenvalues for boundary value problems of fourth-order difference equations Δ4yi=λai+2yi+2, −1≤i≤n−2, y0=Δ2y−1=Δyn=Δ3yn−1=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 aj≥bj, 1≤j≤n, and the existence of positive eigenvector corresponding to the smallest eigenvalue of the problem is also obtained in this paper.