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Trace Formulae for Second-Order Differential Pencils with a Frozen Argument

Author

Listed:
  • Yi-Teng Hu

    (School of Mathematics and Statistics, Xidian University, Xi’an 710126, China)

  • Murat Şat

    (Department of Mathematics, Faculty of Science and Art, Erzincan Binali Yildirim University, Erzincan 24100, Turkey)

Abstract

This paper deals with second-order differential pencils with a fixed frozen argument on a finite interval. We obtain the trace formulae under four boundary conditions: Dirichlet–Dirichlet, Neumann–Neumann, Dirichlet–Neumann, Neumann–Dirichlet. Although the boundary conditions and the corresponding asymptotic behaviour of the eigenvalues are different, the trace formulae have the same form which reveals the impact of the frozen argument.

Suggested Citation

  • Yi-Teng Hu & Murat Şat, 2023. "Trace Formulae for Second-Order Differential Pencils with a Frozen Argument," Mathematics, MDPI, vol. 11(18), pages 1-7, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3996-:d:1243906
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    References listed on IDEAS

    as
    1. Bondarenko, Natalia P., 2022. "Finite-difference approximation of the inverse Sturm–Liouville problem with frozen argument," Applied Mathematics and Computation, Elsevier, vol. 413(C).
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