Eigenvalue comparisons for boundary value problems of the discrete beam equation
- Jun Ji1Email author and
- Bo Yang1
https://doi.org/10.1155/ADE/2006/81025
© Jun Ji and Yang 2006
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≤i≤n-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 ≤ j ≤ n, and the existence of positive eigenvector corresponding to the smallest eigenvalue of the problem is also obtained in this paper.
Keywords
Authors’ Affiliations
References
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