IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i22p2989-d685383.html
   My bibliography  Save this article

Inverse Spectral Problems for Arbitrary-Order Differential Operators with Distribution Coefficients

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)

Abstract

In this paper, we propose an approach to inverse spectral problems for the n -th order ( n ≥ 2 ) ordinary differential operators with distribution coefficients. The inverse problems which consist in the reconstruction of the differential expression coefficients by the Weyl matrix and by several spectra are studied. We prove the uniqueness of solution for these inverse problems, by developing the method of spectral mappings. The results of this paper generalize the previously known results for the second-order differential operators with singular potentials and for the higher-order differential operators with regular coefficients. In the future, the approach of this paper can be used for constructive solution and for investigation of solvability of the considered inverse problems.

Suggested Citation

  • Natalia P. Bondarenko, 2021. "Inverse Spectral Problems for Arbitrary-Order Differential Operators with Distribution Coefficients," Mathematics, MDPI, vol. 9(22), pages 1-17, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2989-:d:685383
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/22/2989/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/22/2989/
    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:22:p:2989-:d:685383. 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.