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 (599.2 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
Research Article | Open Access

Existence of solutions for a coupled Schrödinger equations with critical exponent

Xiaoyong Qian1, Jun Wang2( ), Maochun Zhu1
School of Mathematical of Sciences, Jiangsu University, Zhenjiang, Jiangsu, 212013, China
Institute of Applied System Analysis, Jiangsu University, Zhenjiang, Jiangsu, 212013, China
Show Author Information

Abstract

In this paper we study the existence of multiple nontrivial solutions of the coupled Schrödinger system with external sources terms as perturbations. This type of the system arises from Bose-Einstein condensate. As these external sources terms are nonlinear functions and small in some sense, we use fibre map to divide the Nehari manifold into threes parts, and then prove the existence of a nontrivial ground state solution and a bound state solution.

Keywords

coupled Schrödinger equationsSobolev critical exponentvariational methodNehari Manifold

References

【1】
【1】
 
 
Crossref Google Scholar
Electronic Research Archive
Volume 30 Issue 7,
July 2022
Pages 2730-2747
DOI: 10.3934/era.2022140

{{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:
Qian X, Wang J, Zhu M. Existence of solutions for a coupled Schrödinger equations with critical exponent. Electronic Research Archive, 2022, 30(7): 2730-2747. https://doi.org/10.3934/era.2022140

12

Views

0

Downloads

1

Crossref

1

Web of Science

1

Scopus
Received: 15 September 2021
Revised: 06 March 2022
Accepted: 06 March 2022
Published: 15 July 2022
©2022 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)