IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i12p2070-d839383.html
   My bibliography  Save this article

Existence and Multiplicity of Solutions for a Class of Particular Boundary Value Poisson Equations

Author

Listed:
  • Songyue Yu

    (School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China)

  • Baoqiang Yan

    (School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China)

Abstract

In this paper, a special class of boundary value problems, − ▵ u = λ u q + u r , in Ω , u > 0 , in Ω , n · ∇ u + g ( u ) u = 0 , on ∂ Ω , where 0 < q < 1 < r < N + 2 N − 2 and g : [ 0 , ∞ ) → ( 0 , ∞ ) is a nondecreasing C 1 function. Here, Ω ⊂ R N ( N ≥ 3 ) is a bounded domain with smooth boundary ∂ Ω and λ > 0 is a parameter. The existence of the solution is verified via sub- and super-solutions method. In addition, the influences of parameters on the minimum solution are also discussed. The second positive solution is obtained by using the variational method.

Suggested Citation

  • Songyue Yu & Baoqiang Yan, 2022. "Existence and Multiplicity of Solutions for a Class of Particular Boundary Value Poisson Equations," Mathematics, MDPI, vol. 10(12), pages 1-19, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2070-:d:839383
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/12/2070/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/12/2070/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yansheng Liu, 2013. "Positive Solutions Using Bifurcation Techniques for Boundary Value Problems of Fractional Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, November.
    2. Song-Yue Yu & Baoqiang Yan, 2021. "Positive Solutions for a Singular Elliptic Equation Arising in a Theory of Thermal Explosion," Mathematics, MDPI, vol. 9(17), pages 1-17, September.
    3. Adiqa Kausar Kiani & Wasim Ullah Khan & Muhammad Asif Zahoor Raja & Yigang He & Zulqurnain Sabir & Muhammad Shoaib, 2021. "Intelligent Backpropagation Networks with Bayesian Regularization for Mathematical Models of Environmental Economic Systems," Sustainability, MDPI, vol. 13(17), pages 1-19, August.
    4. Yansheng Liu & Huimin Yu, 2013. "Bifurcation of Positive Solutions for a Class of Boundary Value Problems of Fractional Differential Inclusions," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, March.
    5. Cheng, Hongmei & Yuan, Rong, 2018. "Traveling waves of some Holling–Tanner predator–prey system with nonlocal diffusion," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 12-24.
    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. Kamal Abdelrahim Mohamed Shuka & Wang Ke & Mohammad Sohail Nazar & Ghali Abdullahi Abubakar & AmirReza Shahtahamssebi, 2022. "Impact of Hydrological Infrastructure Projects on Land Use/Cover and Socioeconomic Development in Arid Regions—Evidence from the Upper Atbara and Setit Dam Complex, Kassala, Eastern Sudan," Sustainability, MDPI, vol. 14(6), pages 1-23, March.
    2. Wenyuan Ma & Baoqiang Yan, 2023. "Global Existence and Uniform Blow-Up to a Nonlocal Parabolic System with Nonlinear Boundary Conditions Arising in a Thermal Explosion Theory," Mathematics, MDPI, vol. 11(9), pages 1-22, April.
    3. Zulqurnain Sabir & Atef F. Hashem & Adnène Arbi & Mohamed A. Abdelkawy, 2023. "Designing a Bayesian Regularization Approach to Solve the Fractional Layla and Majnun System," Mathematics, MDPI, vol. 11(17), pages 1-13, September.

    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:10:y:2022:i:12:p:2070-:d:839383. 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.