IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i24p3320-d706530.html
   My bibliography  Save this article

Hyers-Ulam Stability of Euler’s Equation in the Calculus of Variations

Author

Listed:
  • Daniela Marian

    (Department of Mathematics, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania
    These authors contributed equally to this work.)

  • Sorina Anamaria Ciplea

    (Department of Management and Technology, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania
    These authors contributed equally to this work.)

  • Nicolaie Lungu

    (Department of Mathematics, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania
    These authors contributed equally to this work.)

Abstract

In this paper we study Hyers-Ulam stability of Euler’s equation in the calculus of variations in two special cases: when F = F ( x , y ′ ) and when F = F ( y , y ′ ) . For the first case we use the direct method and for the second case we use the Laplace transform. In the first Theorem and in the first Example the corresponding estimations for J y x − J y 0 x are given. We mention that it is the first time that the problem of Ulam-stability of extremals for functionals represented in integral form is studied.

Suggested Citation

  • Daniela Marian & Sorina Anamaria Ciplea & Nicolaie Lungu, 2021. "Hyers-Ulam Stability of Euler’s Equation in the Calculus of Variations," Mathematics, MDPI, vol. 9(24), pages 1-9, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3320-:d:706530
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/24/3320/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/24/3320/
    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:24:p:3320-:d:706530. 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.