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Infinite Homoclinic Solutions of the Discrete Partial Mean Curvature Problem with Unbounded Potential

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  • Yanshan Chen

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

The mean curvature problem is an important class of problems in mathematics and physics. We consider the existence of homoclinic solutions to a discrete partial mean curvature problem, which is tied to the existence of discrete solitons. Under the assumptions that the potential function is unbounded and that the nonlinear term is superlinear at infinity, we obtain the existence of infinitely many homoclinic solutions to this problem by means of the fountain theorem in the critical point theory. In the end, an example is given to illustrate the applicability of our results.

Suggested Citation

  • Yanshan Chen & Zhan Zhou, 2022. "Infinite Homoclinic Solutions of the Discrete Partial Mean Curvature Problem with Unbounded Potential," Mathematics, MDPI, vol. 10(9), pages 1-12, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1436-:d:801169
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    References listed on IDEAS

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