Eigenvalue comparisons for boundary value problems of the discrete beam equation

We study the behavior of all eigenvalues for boundary value problems of fourth-order difference equations Delta(4)yi = lambda a(i+2)y(i+2), - 1 <= i <= n-2, y(0) = Delta(2)y(-1) = Delta yn = Delta(3)y(n-1) = 0, as the sequence {ai}(i=1)(n) varies. A comparison theorem of all eigenvalues is established for two sequences {ai}(i=1)(n) and {b(i)}(i=1)(n) with a(j) >= b(j), 1 <= j <= n, and the existence of positive eigenvector corresponding to the smallest eigenvalue of the problem is also obtained in this paper. Copyright (c) 2006 J. Ji and B. Yang.