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Multiple Solutions for Partial Discrete Dirichlet Problems Involving the p -Laplacian

Author

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  • Sijia Du

    (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

Due to the applications in many fields, there is great interest in studying partial difference equations involving functions with two or more discrete variables. In this paper, we deal with the existence of infinitely many solutions for a partial discrete Dirichlet boundary value problem with the p -Laplacian by using critical point theory. Moreover, under appropriate assumptions on the nonlinear term, we determine open intervals of the parameter such that at least two positive solutions and an unbounded sequence of positive solutions are obtained by using the maximum principle. We also show two examples to illustrate our results.

Suggested Citation

  • Sijia Du & Zhan Zhou, 2020. "Multiple Solutions for Partial Discrete Dirichlet Problems Involving the p -Laplacian," Mathematics, MDPI, vol. 8(11), pages 1-20, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2030-:d:445042
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    Cited by:

    1. Feng Xiong, 2023. "Infinitely Many Solutions for Partial Discrete Kirchhoff Type Problems Involving p -Laplacian," Mathematics, MDPI, vol. 11(15), pages 1-10, July.

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