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Periodic solutions for a second-order partial difference equation

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Abstract

A second-order partial difference equation is considered in this paper. By applying critical point theory, we not only establish a series of sufficient conditions on the existence of periodic solutions when the nonlinearity respectively is superlinear, sublinear and asymptotically linear, but also give sufficient conditions on the nonexistence of nontrivial periodic solutions. Finally, we present some examples to illustrate our main results.

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Acknowledgements

The authors gratefully acknowledge the two anonymous reviewers for their careful reading and valuable comments and suggestions.

Funding

This work was supported by the National Natural Science Foundation of China (Grant No. 11971126), the Program for Changjiang Scholars and Innovative Research Team in University (Grant No. IRT 16R16) and the Innovation Research for the Postgraduates of Guangzhou University (Grant No. 2021GDJC-D06).

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Author notes

  1. Shaohong Wang have contributed equally to this work.

Authors and Affiliations

  1. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China

    Shaohong Wang & Zhan Zhou

  2. Guangzhou Center for Applied Mathematics, Guangzhou University, Guangzhou, 510006, China

    Shaohong Wang & Zhan Zhou

Authors
  1. Shaohong Wang
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  2. Zhan Zhou
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Contributions

Conceptualization: Shaohong Wang; Methodology: Shaohong Wang; Formal analysis and investigation: Shaohong Wang, Zhan Zhou; Writing—original draft preparation: Shaohong Wang; Writing—review and editing: Zhan Zhou; Funding acquisition: Zhan Zhou; Supervision: Zhan Zhou.

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Correspondence to Zhan Zhou.

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Wang, S., Zhou, Z. Periodic solutions for a second-order partial difference equation. J. Appl. Math. Comput. 69, 731–752 (2023). https://doi.org/10.1007/s12190-022-01769-0

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  • DOI: https://doi.org/10.1007/s12190-022-01769-0

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