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Positive Solutions of Boundary Value Problems for General Second-Order Nonlinear Difference Equations

Author

Listed:
  • Ruoyi Liu

    (School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China)

  • Zhan Zhou

    (School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
    Guangzhou Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China)

Abstract

In this paper, we investigate positive solutions of boundary value problems for a general second-order nonlinear difference equation, which includes a Jacobi operator and a parameter λ . Based on the critical point theory, we obtain the existence of three solutions for the boundary value problem. Then, we establish a strong maximum principle for this problem and obtain some determined open intervals of the parameter λ for the existence of at least two positive solutions. In the end, we give two examples to illustrate our main results.

Suggested Citation

  • Ruoyi Liu & Zhan Zhou, 2024. "Positive Solutions of Boundary Value Problems for General Second-Order Nonlinear Difference Equations," Mathematics, MDPI, vol. 12(23), pages 1-16, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3770-:d:1532875
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    References listed on IDEAS

    as
    1. Jianye Xia & Yuji Liu, 2011. "Solvability of a Class of Generalized Neumann Boundary Value Problems for Second-Order Nonlinear Difference Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-11, August.
    2. Bahua Lin & Zhan Zhou, 2023. "Positive Solutions to the Discrete Boundary Value Problem of the Kirchhoff Type," Mathematics, MDPI, vol. 11(16), pages 1-14, August.
    3. Xia Liu & Tao Zhou & Haiping Shi, 2018. "Existence and Nonexistence of Solutions for Fourth-Order Nonlinear Difference Boundary Value Problems via Variational Methods," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-9, September.
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