IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i19p2999-d1486477.html
   My bibliography  Save this article

Instability of Standing Waves for INLS with Inverse Square Potential

Author

Listed:
  • Saleh Almuthaybiri

    (Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia)

  • Tarek Saanouni

    (Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia)

Abstract

This work studies an inhomogeneous generalized Hartree equation with inverse square potential. The purpose is to prove the existence and strong instability of inter-critical standing waves. This means that there are infinitely many data near to the ground state, such that the associated solution blows-up in finite time. The proof combines a variational analysis with the standard variance identity. The challenge is to deal with three difficulties: the singular potential | x | − 2 , an inhomogeneous term | x | − λ , and a non-local source term.

Suggested Citation

  • Saleh Almuthaybiri & Tarek Saanouni, 2024. "Instability of Standing Waves for INLS with Inverse Square Potential," Mathematics, MDPI, vol. 12(19), pages 1-12, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:2999-:d:1486477
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/19/2999/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/19/2999/
    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:12:y:2024:i:19:p:2999-:d:1486477. 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.