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Research Article | Open Access

On periodic solutions of second-order partial difference equations involving p-Laplacian

Dan Li1, Yuhua Long1,2( )
School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, P. R. China
Center for Applied Mathematics, Guangzhou University, Guangzhou, 510006, P. R. China
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Abstract

By combining variational techniques with the saddle point theorem, we investigate the existence and nonexistence of periodic solutions to second-order partial difference equations involving p-Laplacians. Our obtained results generalize and complement some known ones. Finally, we display some examples and numerical simulations to show the validity of our main results.

Keywords

existencenonexistenceperiodic solutionpartial difference equation involving p-Laplacianvariational method
CLC number: 39A14, 34C37

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Communications in Analysis and Mechanics
Volume 17 Issue 1,
March 2025
Pages 128-144
DOI: 10.3934/cam.2025006

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Cite this article:
Li D, Long Y. On periodic solutions of second-order partial difference equations involving p-Laplacian. Communications in Analysis and Mechanics, 2025, 17(1): 128-144. https://doi.org/10.3934/cam.2025006

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Received: 19 January 2024
Revised: 19 November 2024
Accepted: 07 January 2025
Published: 15 March 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)