Results on multiple nontrivial solutions to partial difference equations

Huan Zhang; Yin Zhou; Yuhua Long; Huan Zhang; Yin Zhou; Yuhua Long

doi:10.3934/math.2023272

AIMS Mathematics

2023, Volume 8, Issue 3: 5413-5431. doi: 10.3934/math.2023272

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Results on multiple nontrivial solutions to partial difference equations

1.
School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China
2.
Guangzhou University, Guangzhou Center for Applied Mathematics, Guangzhou, 510006, China
3.
Transportation and Economics Research Institute of China Academy of Railway Sciences Corporation Limited, Beijing, 100081, China

Received: 25 August 2022 Revised: 12 December 2022 Accepted: 12 December 2022 Published: 16 December 2022
MSC : 34B15, 35B38, 39A10

In this paper, we consider the existence and multiplicity of nontrivial solutions to second order partial difference equation with Dirichlet boundary conditions by Morse theory. Given suitable conditions, we establish multiple results that the problem admits at least two nontrivial solutions. Moreover, we provide five examples to illustrate applications of our theorems.
- partial difference equation,
- local linking,
- Morse theory,
- nontrivial solution
Citation: Huan Zhang, Yin Zhou, Yuhua Long. Results on multiple nontrivial solutions to partial difference equations[J]. AIMS Mathematics, 2023, 8(3): 5413-5431. doi: 10.3934/math.2023272

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Abstract

In this paper, we consider the existence and multiplicity of nontrivial solutions to second order partial difference equation with Dirichlet boundary conditions by Morse theory. Given suitable conditions, we establish multiple results that the problem admits at least two nontrivial solutions. Moreover, we provide five examples to illustrate applications of our theorems.

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