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Research Article | Open Access

The uniqueness of solutions for a singular Kirchhoff equation with the Kohn–Laplace operator

School of Sciences, Guizhou University of Engineering Science, Bijie 551700, China
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Abstract

In this paper, we use the minimax method and certain analysis techniques to establish the uniqueness of solutions for a class of (strongly) singular Kirchhoff equations with the Kohn–Laplace operator in the n-Heisenberg group and further deduce that the solution is cylindrically symmetric under some necessary structural conditions for a Kohn–Laplace equation with singularity.

Keywords

Heisenberg groupKohn–Laplaciansingular nonlinearityuniqueness of solutions
CLC number: 35B09, 35B32

References

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AIMS Mathematics
Volume 11 Issue 5,
May 2026
Pages 14474-14486
DOI: 10.3934/math.2026593

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An Y-C. The uniqueness of solutions for a singular Kirchhoff equation with the Kohn–Laplace operator. AIMS Mathematics, 2026, 11(5): 14474-14486. https://doi.org/10.3934/math.2026593

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Received: 24 March 2026
Revised: 06 May 2026
Accepted: 11 May 2026
Published: 15 May 2026
©2026 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)