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Research Article | Open Access

Existence and multiplicity of nontrivial solutions to discrete elliptic Dirichlet problems

Yuhua Long1,2( ), Huan Zhang1,2
School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
Guangzhou University, Guangzhou Center for Applied Mathematics, Guangzhou 510006, China
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Abstract

In this paper, we study discrete elliptic Dirichlet problems. Applying a variational technique together with Morse theory, we establish several results on the existence and multiplicity of nontrivial solutions. Finally, two examples and numerical simulations are provided to illustrate our theoretical results.

Keywords

discrete elliptic Dirichlet problemlocal linkingMorse theorynontrivial solution

References

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Electronic Research Archive
Volume 30 Issue 7,
July 2022
Pages 2681-2699
DOI: 10.3934/era.2022137

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Cite this article:
Long Y, Zhang H. Existence and multiplicity of nontrivial solutions to discrete elliptic Dirichlet problems. Electronic Research Archive, 2022, 30(7): 2681-2699. https://doi.org/10.3934/era.2022137

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Received: 15 April 2022
Revised: 06 May 2022
Accepted: 09 May 2022
Published: 15 July 2022
©2022 the Author(s), licensee AIMS Press.

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