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Research Article | Open Access

Multiple solutions to a nonlocal sub-Laplacian system with critical growth and logarithmic perturbation

Yu-Cheng An1( ), Bi-Jun An2
School of Sciences, Guizhou University of Engineering Science, Bijie 551700, Guizhou, China
School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, Guizhou, China
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Abstract

In this paper, we studied the existence of solutions for a nonlocal sub-Laplacian system with critical growth and logarithmic perturbation. That is to say, by using the symmetric mountain pass lemma, we proved that under some suitable conditions, the nonlocal sub-Laplacian system admits a sequence { z k } of nontrivial solutions satisfying lim k → ∞ z k = 0. To the best of our knowledge, this result is new even in the Euclidean case.

Keywords

sub-Laplacian systemcritical growthlogarithmic perturbationsymmetric mountain pass lemmamultiple solutionsHeisenberg group
CLC number: 35J20, 35H20

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AIMS Mathematics
Volume 10 Issue 5,
May 2025
Pages 10605-10623
DOI: 10.3934/math.2025482

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Cite this article:
An Y-C, An B-J. Multiple solutions to a nonlocal sub-Laplacian system with critical growth and logarithmic perturbation. AIMS Mathematics, 2025, 10(5): 10605-10623. https://doi.org/10.3934/math.2025482

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Received: 22 March 2025
Revised: 21 April 2025
Accepted: 27 April 2025
Published: 15 May 2025
©2025 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)