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Research Article | Open Access

Results on multiple nontrivial solutions to partial difference equations

Huan Zhang1,2, Yin Zhou3, Yuhua Long1,2( )
School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China
Guangzhou University, Guangzhou Center for Applied Mathematics, Guangzhou, 510006, China
Transportation and Economics Research Institute of China Academy of Railway Sciences Corporation Limited, Beijing, 100081, China
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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.

Keywords

partial difference equationlocal linkingMorse theorynontrivial solution
CLC number: 34B15, 35B38, 39A10

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AIMS Mathematics
Volume 8 Issue 3,
March 2023
Pages 5413-5431
DOI: 10.3934/math.2023272

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Cite this article:
Zhang H, Zhou Y, Long Y. Results on multiple nontrivial solutions to partial difference equations. AIMS Mathematics, 2023, 8(3): 5413-5431. https://doi.org/10.3934/math.2023272

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Received: 25 August 2022
Revised: 12 December 2022
Accepted: 12 December 2022
Published: 15 March 2023
©2023 the Author(s), licensee AIMS Press.

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