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Positive Solutions to the Discrete Boundary Value Problem of the Kirchhoff Type

Author

Listed:
  • Bahua Lin

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

  • Zhan Zhou

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

Abstract

The paper aims to study a discrete boundary value problem of the Kirchhoff type based on the critical point theory and the strong maximum principle. Compared to the existing literature, the existence and multiplicity of positive solutions to the problem are considered according to the behavior of the nonlinear term f in some points between the zero and positive infinity, which is a new attempt. Under different assumptions of the nonlinear term f , we obtain the determined open intervals of the parameter λ , such that the problem has at least three positive solutions or at least two positive solutions in different intervals. In the end, two concrete examples are used to illustrate our main conclusions.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3588-:d:1220471
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    References listed on IDEAS

    as
    1. Ruofeng Rao & Zhi Lin & Xiaoquan Ai & Jiarui Wu, 2022. "Synchronization of Epidemic Systems with Neumann Boundary Value under Delayed Impulse," Mathematics, MDPI, vol. 10(12), pages 1-10, June.
    2. Chunsheng Wang & Xiangdong Liu & Feng Jiao & Hong Mai & Han Chen & Runpeng Lin, 2023. "Generalized Halanay Inequalities and Relative Application to Time-Delay Dynamical Systems," Mathematics, MDPI, vol. 11(8), pages 1-11, April.
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