IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i17p3754-d1230308.html
   My bibliography  Save this article

Existence of Solutions for Planar Kirchhoff–Choquard Problems

Author

Listed:
  • Rui Niu

    (College of Science, Heilongjiang Institute of Technology, Harbin 150050, China)

  • Tianxing Wu

    (No. 703 Research Institute, China State Shipbuilding Co., Ltd., Harbin 150078, China)

Abstract

In this article, we are interested in the study of the following Kirchhoff–Choquard equations: − a + b ∫ R 2 | ∇ u | 2 d x Δ u + V ( x ) u = λ ( ln | x | ∗ u 2 ) u + f ( u ) , x ∈ R 2 , where λ > 0 , a > 0 , b > 0 , V and f are continuous functions with some appropriate assumptions. We prove that when the parameter λ is sufficiently small, the above problem has a mountain pass solution, a least energy solution and a ground state solution by applying the variational methods and building some subtle inequalities.

Suggested Citation

  • Rui Niu & Tianxing Wu, 2023. "Existence of Solutions for Planar Kirchhoff–Choquard Problems," Mathematics, MDPI, vol. 11(17), pages 1-19, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3754-:d:1230308
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/17/3754/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/17/3754/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Chun-Yu Lei & Gao-Sheng Liu, 2021. "Near resonance for a Kirchhoff–Schrödinger–Newton system," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(2), pages 363-368, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      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:11:y:2023:i:17:p:3754-:d:1230308. 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.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.