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Theory Article | Open Access

Existence of positive solution for critical Schrödinger-Poisson system on the first Heisenberg group

Xuechun Zheng1, Lifeng Guo1, Sihua Liang1,2( )
School of Mathematics and Statistics, Northeast Petroleum University, Daqing 163711, China
College of Mathematics, Changchun Normal University, Changchun 130123, China
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Abstract

In this article, we consider a class of critical Schrödinger-Poisson type systems on the first Heisenberg group. We demonstrate that the system admits a positive ground state solution by utilizing the concentration compactness principle and critical point theory. The system has double critical nonlinearity on the Heisenberg group, which is the novelty and peculiarity of this paper. To some extent, we extend some previous results.

Keywords

Heisenberg groupSchrödinger-Poisson systemconcentration-compactness principlevariational methods

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Electronic Research Archive
Volume 33 Issue 11,
November 2025
Pages 7052-7064
DOI: 10.3934/era.2025311

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Cite this article:
Zheng X, Guo L, Liang S. Existence of positive solution for critical Schrödinger-Poisson system on the first Heisenberg group. Electronic Research Archive, 2025, 33(11): 7052-7064. https://doi.org/10.3934/era.2025311

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Received: 13 September 2025
Revised: 05 November 2025
Accepted: 11 November 2025
Published: 21 November 2025
©2025 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)