IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i23p3869-d1539905.html
   My bibliography  Save this article

Multiple and Nonexistence of Positive Solutions for a Class of Fractional Differential Equations with p -Laplacian Operator

Author

Listed:
  • Haoran Zhang

    (School of Mathematical Sciences, Qufu Normal University, Jining 273165, China)

  • Zhaocai Hao

    (School of Mathematical Sciences, Qufu Normal University, Jining 273165, China)

  • Martin Bohner

    (Department of Mathematics and Statistics, Missouri S&T, Rolla, MO 65409-0020, USA)

Abstract

Research about multiple positive solutions for fractional differential equations is very important. Based on some outstanding results reported in this field, this paper continue the focus on this topic. By using the properties of the Green function and generalized Avery–Henderson fixed point theorem, we derive three positive solutions of a class of fractional differential equations with a p -Laplacian operator. We also study the nonexistence of positive solutions to the eigenvalue problem of the equation. Three examples are given to illustrate our main result.

Suggested Citation

  • Haoran Zhang & Zhaocai Hao & Martin Bohner, 2024. "Multiple and Nonexistence of Positive Solutions for a Class of Fractional Differential Equations with p -Laplacian Operator," Mathematics, MDPI, vol. 12(23), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3869-:d:1539905
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/23/3869/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/23/3869/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jinhua Wang & Hongjun Xiang, 2010. "Upper and Lower Solutions Method for a Class of Singular Fractional Boundary Value Problems with p -Laplacian Operator," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-12, September.
    2. Han, Zhenlai & Lu, Hongling & Zhang, Chao, 2015. "Positive solutions for eigenvalue problems of fractional differential equation with generalized p-Laplacian," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 526-536.
    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.
    1. Wenquan Wu & Xiangbing Zhou, 2013. "Eigenvalue of Fractional Differential Equations with -Laplacian Operator," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-8, March.
    2. Liu, Xiping & Jia, Mei, 2019. "Solvability and numerical simulations for BVPs of fractional coupled systems involving left and right fractional derivatives," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 230-242.
    3. Li, Xiaoyan, 2021. "Comment for “Existence and Hyers-Ulam stability for a nonlinear singular fractional differential equations with Mittag-Leffler kernel”," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).

    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:23:p:3869-:d:1539905. 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.