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Research Article | Open Access

Existence and nonexistence of positive solutions to a class of nonlocal discrete Kirchhoff type equations

School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
Guangzhou Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China
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Abstract

In this paper, we investigate the existence and nonexistence of positive solutions to a class of nonlocal partial difference equations via a variant version of the mountain pass theorem. The conditions in our obtained results release the classical (AR) condition in some sense.

Keywords

difference equationpositive solutionmountain pass theoremexistencenonexistence
CLC number: 39A10, 34B15, 35B38

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AIMS Mathematics
Volume 8 Issue 10,
October 2023
Pages 24568-24589
DOI: 10.3934/math.20231253

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Cite this article:
Long Y. Existence and nonexistence of positive solutions to a class of nonlocal discrete Kirchhoff type equations. AIMS Mathematics, 2023, 8(10): 24568-24589. https://doi.org/10.3934/math.20231253

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Received: 11 May 2023
Revised: 07 August 2023
Accepted: 15 August 2023
Published: 15 October 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)