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

Yu-Cheng An; Yu-Cheng An

doi:10.3934/math.2026593

AIMS Mathematics

2026, Volume 11, Issue 5: 14474-14486. doi: 10.3934/math.2026593

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Research article

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

Yu-Cheng An ^,

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

Received: 24 March 2026 Revised: 06 May 2026 Accepted: 11 May 2026 Published: 22 May 2026
MSC : 35B09, 35B32

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.
- Heisenberg group,
- Kohn–Laplacian,
- singular nonlinearity,
- uniqueness of solutions
Citation: Yu-Cheng An. The uniqueness of solutions for a singular Kirchhoff equation with the Kohn–Laplace operator[J]. AIMS Mathematics, 2026, 11(5): 14474-14486. doi: 10.3934/math.2026593

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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.

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