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Three Solutions for a Partial Discrete Dirichlet Problem Involving the Mean Curvature Operator

Author

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  • Shaohong Wang

    (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

Partial difference equations have received more and more attention in recent years due to their extensive applications in diverse areas. In this paper, we consider a Dirichlet boundary value problem of the partial difference equation involving the mean curvature operator. By applying critical point theory, the existence of at least three solutions is obtained. Furthermore, under some appropriate assumptions on the nonlinearity, we respectively show that this problem admits at least two or three positive solutions by means of a strong maximum principle. Finally, we present two concrete examples and combine with images to illustrate our main results.

Suggested Citation

  • Shaohong Wang & Zhan Zhou, 2021. "Three Solutions for a Partial Discrete Dirichlet Problem Involving the Mean Curvature Operator," Mathematics, MDPI, vol. 9(14), pages 1-20, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:14:p:1691-:d:596888
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    References listed on IDEAS

    as
    1. Sugie, Jitsuro, 2021. "Number of positive periodic solutions for first-order nonlinear difference equations with feedback," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    2. Durhasan Turgut Tollu & Hijaz Ahmad, 2020. "Periodic Solutions of a System of Nonlinear Difference Equations with Periodic Coefficients," Journal of Mathematics, Hindawi, vol. 2020, pages 1-7, December.
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