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

Xuechun Zheng; Lifeng Guo; Sihua Liang; Xuechun Zheng; Lifeng Guo; Sihua Liang

doi:10.3934/era.2025311

Electronic Research Archive

2025, Volume 33, Issue 11: 7052-7064. doi: 10.3934/era.2025311

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

1.
School of Mathematics and Statistics, Northeast Petroleum University, Daqing 163711, China
2.
College of Mathematics, Changchun Normal University, Changchun 130123, China

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

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.
- Heisenberg group,
- Schrödinger-Poisson system,
- concentration-compactness principle,
- variational methods
Citation: Xuechun Zheng, Lifeng Guo, Sihua Liang. Existence of positive solution for critical Schrödinger-Poisson system on the first Heisenberg group[J]. Electronic Research Archive, 2025, 33(11): 7052-7064. doi: 10.3934/era.2025311

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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.

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