Multiple nontrivial periodic solutions to a second-order partial difference equation

Yuhua Long; Dan Li; Yuhua Long; Dan Li

doi:10.3934/era.2023082

Electronic Research Archive

2023, Volume 31, Issue 3: 1596-1612. doi: 10.3934/era.2023082

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Multiple nontrivial periodic solutions to a second-order partial difference equation

Yuhua Long ^{1,2
,
,},
Dan Li ^1,2

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

Received: 21 October 2022 Revised: 09 January 2023 Accepted: 15 January 2023 Published: 31 January 2023

In this article, applying variational technique as well as critical point theory, we establish a series of criteria to ensure the existence and multiplicity of nontrivial periodic solutions to a second-order nonlinear partial difference equation. Our results generalize some known results. Moreover, numerical stimulations are presented to illustrate applications of our major findings.
- critical point theory,
- partial difference equation,
- nontrivial periodic solutions,
- variational technique
Citation: Yuhua Long, Dan Li. Multiple nontrivial periodic solutions to a second-order partial difference equation[J]. Electronic Research Archive, 2023, 31(3): 1596-1612. doi: 10.3934/era.2023082

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Abstract

In this article, applying variational technique as well as critical point theory, we establish a series of criteria to ensure the existence and multiplicity of nontrivial periodic solutions to a second-order nonlinear partial difference equation. Our results generalize some known results. Moreover, numerical stimulations are presented to illustrate applications of our major findings.

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