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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 Δ4y i = λai+2yi+2, -1≤in-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 ≤ jn, and the existence of positive eigenvector corresponding to the smallest eigenvalue of the problem is also obtained in this paper.

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Correspondence to Jun Ji.

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Ji, J., Yang, B. Eigenvalue comparisons for boundary value problems of the discrete beam equation. Adv Differ Equ 2006, 081025 (2006). https://doi.org/10.1155/ADE/2006/81025

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Functional Equation
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