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

Dan Li; Yuhua Long; Dan Li; Yuhua Long

doi:10.3934/cam.2025006

Communications in Analysis and Mechanics

2025, Volume 17, Issue 1: 128-144. doi: 10.3934/cam.2025006

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

Dan Li ¹,
Yuhua Long ^{1,2
,
,}

1.
School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, P. R. China
2.
Center for Applied Mathematics, Guangzhou University, Guangzhou, 510006, P. R. China

Received: 19 January 2024 Revised: 19 November 2024 Accepted: 07 January 2025 Published: 10 February 2025
39A14, 34C37

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.
- existence,
- nonexistence,
- periodic solution,
- partial difference equation involving p-Laplacian,
- variational method
Citation: Dan Li, Yuhua Long. On periodic solutions of second-order partial difference equations involving p-Laplacian[J]. Communications in Analysis and Mechanics, 2025, 17(1): 128-144. doi: 10.3934/cam.2025006

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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.

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