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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
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
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