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<p>This paper investigates the dependence of the eigenvalues for fourth-order differential operators with canonical boundary and transmission conditions. We establish that the eigenvalues depend continuously on the problem parameters under standard topological assumptions. Furthermore, we derive explicit expressions for the derivatives of the eigenvalues with respect to the parameters, considering both ordinary and Fréchet derivatives.</p>

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Eigenvalue Dependence in Fourth-Order Differential Operators with Canonical Boundary and Transmission Conditions

  • 期刊论文

  • 发表日期：

    2026年1月31日

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  • Huan Hao,
  • Xiaoling Hao,
  • Kun Li

摘要

This paper investigates the dependence of the eigenvalues for fourth-order differential operators with canonical boundary and transmission conditions. We establish that the eigenvalues depend continuously on the problem parameters under standard topological assumptions. Furthermore, we derive explicit expressions for the derivatives of the eigenvalues with respect to the parameters, considering both ordinary and Fréchet derivatives.