AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home Electronic Research Archive Article
PDF (513.6 KB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
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
Show Author Information

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

References

【1】
【1】
 
 
Crossref Google Scholar
Electronic Research Archive
Volume 33 Issue 11,
November 2025
Pages 7052-7064
DOI: 10.3934/era.2025311

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
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

275

Views

4

Downloads

1

Crossref

2

Web of Science

1

Scopus
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)