IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i20p2617-d658235.html
   My bibliography  Save this article

Solvability and Stability of the Inverse Problem for the Quadratic Differential Pencil

Author

Listed:
  • Natalia P. Bondarenko

    (Department of Applied Mathematics and Physics, Samara National Research University, Moskovskoye Shosse 34, 443086 Samara, Russia
    Department of Mechanics and Mathematics, Saratov State University, Astrakhanskaya 83, 410012 Saratov, Russia)

  • Andrey V. Gaidel

    (Department of Mechanics and Mathematics, Saratov State University, Astrakhanskaya 83, 410012 Saratov, Russia
    Department of Technical Cybernetics, Samara National Research University, Moskovskoye Shosse 34, 443086 Samara, Russia
    Department of Video Mining, IPSI RAS—Branch of the FSRC “Crystallography and Photonics” RAS, Molodogvardeyskaya 151, 443001 Samara, Russia)

Abstract

The inverse spectral problem for the second-order differential pencil with quadratic dependence on the spectral parameter is studied. We obtain sufficient conditions for the global solvability of the inverse problem, prove its local solvability and stability. The problem is considered in the general case of complex-valued pencil coefficients and arbitrary eigenvalue multiplicities. Studying local solvability and stability, we take the possible splitting of multiple eigenvalues under a small perturbation of the spectrum into account. Our approach is constructive. It is based on the reduction of the non-linear inverse problem to a linear equation in the Banach space of infinite sequences. The theoretical results are illustrated by numerical examples.

Suggested Citation

  • Natalia P. Bondarenko & Andrey V. Gaidel, 2021. "Solvability and Stability of the Inverse Problem for the Quadratic Differential Pencil," Mathematics, MDPI, vol. 9(20), pages 1-25, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:20:p:2617-:d:658235
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/20/2617/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/20/2617/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:20:p:2617-:d:658235. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.