Multiple periodic solutions of a class of second-order partial difference equations via Morse theory

Yuhua Long; Baojie Lin; Yuhua Long; Baojie Lin

doi:10.3934/era.2026257

Electronic Research Archive

2026, Volume 34, Issue 8: 5795-5812. doi: 10.3934/era.2026257

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Multiple periodic solutions of a class of second-order partial difference equations via Morse theory

Yuhua Long ^{1,2
,
,},
Baojie Lin ¹

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

Received: 06 May 2026 Revised: 03 June 2026 Accepted: 25 June 2026 Published: 07 July 2026

Based on Morse theory and the mountain pass lemma, we investigate the existence and multiplicity of nontrivial periodic solutions for a class of second-order partial difference equations. If the nonlinearity is resonant or sublinear at infinity, a series of results under reasonable assumptions are established. Also, two examples are provided to illustrate our main results. Our obtained results generalize and improve some existing ones.
- partial difference equation,
- nontrivial periodic solution,
- Morse theory,
- mountain pass lemma,
- resonance,
- sublinear
Citation: Yuhua Long, Baojie Lin. Multiple periodic solutions of a class of second-order partial difference equations via Morse theory[J]. Electronic Research Archive, 2026, 34(8): 5795-5812. doi: 10.3934/era.2026257

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Abstract

Based on Morse theory and the mountain pass lemma, we investigate the existence and multiplicity of nontrivial periodic solutions for a class of second-order partial difference equations. If the nonlinearity is resonant or sublinear at infinity, a series of results under reasonable assumptions are established. Also, two examples are provided to illustrate our main results. Our obtained results generalize and improve some existing ones.

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