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Dependence of eigenvalues for higher odd-order boundary value problems

Author

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  • Ji, Antong
  • Xu, Meizhen

Abstract

This paper is concerned with higher odd-order boundary value problems. We first prove that the operators associated with the problems are symmetric and the corresponding eigenvalues are real, and we give the resolvent operators related to the differential operators. Then we obtain that the eigenvalues are not only continuously but also smoothly dependent on the parameters of the problem. Moreover, the differential expressions of the eigenvalues as regards these parameters are given. In particular, we give the Frechet derivatives of the eigenvalues for the leading coefficient function q0 and coefficient functions q1,⋯,qn.

Suggested Citation

  • Ji, Antong & Xu, Meizhen, 2024. "Dependence of eigenvalues for higher odd-order boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 467(C).
    • Handle: RePEc:eee:apmaco:v:467:y:2024:i:c:s0096300323006562
    DOI: 10.1016/j.amc.2023.128487
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    References listed on IDEAS

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    1. Zhang, Maozhu & Li, Kun, 2020. "Dependence of eigenvalues of Sturm–Liouville problems with eigenparameter dependent boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    2. Zhang, Maozhu & Wang, Yicao, 2015. "Dependence of eigenvalues of Sturm– Liouville problems with interface conditions," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 31-39.
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    2. Zhang, Maozhu & Li, Kun, 2020. "Dependence of eigenvalues of Sturm–Liouville problems with eigenparameter dependent boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 378(C).

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