Journal article 187 views
Schrödinger–Bopp–Podolsky System with Steep Potential Well
Qualitative Theory of Dynamical Systems, Volume: 22, Issue: 4
Swansea University Author: Chenggui Yuan
DOI (Published version): 10.1007/s12346-023-00835-7
Abstract
In this paper, we study the following Schrödinger–Bopp–Podolsky system: {-Δu+λV(x)u+q2φu=f(u)-Δφ+a2Δ2φ=4πu2, where u, φ: R3→ R , a>0,q>0 , λ is real positive parameter, f satisfies supper 2 lines growth. V∈ C(R3, R) , which suppose that V(x) repersents a potential well with the bottom V- 1(0)...
Published in: | Qualitative Theory of Dynamical Systems |
---|---|
ISSN: | 1575-5460 1662-3592 |
Published: |
Springer Science and Business Media LLC
2023
|
Online Access: |
Check full text
|
URI: | https://cronfa.swan.ac.uk/Record/cronfa64044 |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
first_indexed |
2023-08-08T10:17:05Z |
---|---|
last_indexed |
2023-08-08T10:17:05Z |
id |
cronfa64044 |
recordtype |
SURis |
fullrecord |
<?xml version="1.0" encoding="utf-8"?><rfc1807 xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema"><bib-version>v2</bib-version><id>64044</id><entry>2023-08-08</entry><title>Schrödinger–Bopp–Podolsky System with Steep Potential Well</title><swanseaauthors><author><sid>22b571d1cba717a58e526805bd9abea0</sid><ORCID>0000-0003-0486-5450</ORCID><firstname>Chenggui</firstname><surname>Yuan</surname><name>Chenggui Yuan</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2023-08-08</date><deptcode>SMA</deptcode><abstract>In this paper, we study the following Schrödinger–Bopp–Podolsky system: {-Δu+λV(x)u+q2φu=f(u)-Δφ+a2Δ2φ=4πu2, where u, φ: R3→ R , a>0,q>0 , λ is real positive parameter, f satisfies supper 2 lines growth. V∈ C(R3, R) , which suppose that V(x) repersents a potential well with the bottom V- 1(0) . There are no results of solutions for the system with steep potential well in the current literature because of the presence of the nonlocal term. Throughout the truncation technique and the parameter-dependent compactness lemma, we get a poistive energy solution uλ,q for λ large and q small. In the last part, we explore the asymptotic behavior as q→ 0 , λ→ + ∞ .</abstract><type>Journal Article</type><journal>Qualitative Theory of Dynamical Systems</journal><volume>22</volume><journalNumber>4</journalNumber><paginationStart/><paginationEnd/><publisher>Springer Science and Business Media LLC</publisher><placeOfPublication/><isbnPrint/><isbnElectronic/><issnPrint>1575-5460</issnPrint><issnElectronic>1662-3592</issnElectronic><keywords>Schrödinger-Bopp-Podolsky system, Truncation technique, Parameter-dependentcompactness lemma, Asymptotic behavior</keywords><publishedDay>31</publishedDay><publishedMonth>12</publishedMonth><publishedYear>2023</publishedYear><publishedDate>2023-12-31</publishedDate><doi>10.1007/s12346-023-00835-7</doi><url>http://dx.doi.org/10.1007/s12346-023-00835-7</url><notes/><college>COLLEGE NANME</college><department>Mathematics</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>SMA</DepartmentCode><institution>Swansea University</institution><apcterm/><funders>This work was supported by the National Natural Science Foundation of China (Grant Nos. 11661053, 11771198, 11901276 and 11961045) and the Provincial Natural Science Foundation of Jiangxi, China (20181BAB201003, 20202BAB201001 and 20202BAB211004).</funders><projectreference/><lastEdited>2023-09-12T14:47:23.4053841</lastEdited><Created>2023-08-08T11:12:26.3747003</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Mathematics and Computer Science - Mathematics</level></path><authors><author><firstname>Qiutong</firstname><surname>Zhu</surname><order>1</order></author><author><firstname>Chunfang</firstname><surname>Chen</surname><order>2</order></author><author><firstname>Chenggui</firstname><surname>Yuan</surname><orcid>0000-0003-0486-5450</orcid><order>3</order></author></authors><documents><document><filename>Under embargo</filename><originalFilename>Under embargo</originalFilename><uploaded>2023-08-31T15:24:53.4699900</uploaded><type>Output</type><contentLength>360453</contentLength><contentType>application/pdf</contentType><version>Accepted Manuscript</version><cronfaStatus>true</cronfaStatus><embargoDate>2024-07-28T00:00:00.0000000</embargoDate><copyrightCorrect>false</copyrightCorrect><language>eng</language></document></documents><OutputDurs/></rfc1807> |
spelling |
v2 64044 2023-08-08 Schrödinger–Bopp–Podolsky System with Steep Potential Well 22b571d1cba717a58e526805bd9abea0 0000-0003-0486-5450 Chenggui Yuan Chenggui Yuan true false 2023-08-08 SMA In this paper, we study the following Schrödinger–Bopp–Podolsky system: {-Δu+λV(x)u+q2φu=f(u)-Δφ+a2Δ2φ=4πu2, where u, φ: R3→ R , a>0,q>0 , λ is real positive parameter, f satisfies supper 2 lines growth. V∈ C(R3, R) , which suppose that V(x) repersents a potential well with the bottom V- 1(0) . There are no results of solutions for the system with steep potential well in the current literature because of the presence of the nonlocal term. Throughout the truncation technique and the parameter-dependent compactness lemma, we get a poistive energy solution uλ,q for λ large and q small. In the last part, we explore the asymptotic behavior as q→ 0 , λ→ + ∞ . Journal Article Qualitative Theory of Dynamical Systems 22 4 Springer Science and Business Media LLC 1575-5460 1662-3592 Schrödinger-Bopp-Podolsky system, Truncation technique, Parameter-dependentcompactness lemma, Asymptotic behavior 31 12 2023 2023-12-31 10.1007/s12346-023-00835-7 http://dx.doi.org/10.1007/s12346-023-00835-7 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University This work was supported by the National Natural Science Foundation of China (Grant Nos. 11661053, 11771198, 11901276 and 11961045) and the Provincial Natural Science Foundation of Jiangxi, China (20181BAB201003, 20202BAB201001 and 20202BAB211004). 2023-09-12T14:47:23.4053841 2023-08-08T11:12:26.3747003 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Qiutong Zhu 1 Chunfang Chen 2 Chenggui Yuan 0000-0003-0486-5450 3 Under embargo Under embargo 2023-08-31T15:24:53.4699900 Output 360453 application/pdf Accepted Manuscript true 2024-07-28T00:00:00.0000000 false eng |
title |
Schrödinger–Bopp–Podolsky System with Steep Potential Well |
spellingShingle |
Schrödinger–Bopp–Podolsky System with Steep Potential Well Chenggui Yuan |
title_short |
Schrödinger–Bopp–Podolsky System with Steep Potential Well |
title_full |
Schrödinger–Bopp–Podolsky System with Steep Potential Well |
title_fullStr |
Schrödinger–Bopp–Podolsky System with Steep Potential Well |
title_full_unstemmed |
Schrödinger–Bopp–Podolsky System with Steep Potential Well |
title_sort |
Schrödinger–Bopp–Podolsky System with Steep Potential Well |
author_id_str_mv |
22b571d1cba717a58e526805bd9abea0 |
author_id_fullname_str_mv |
22b571d1cba717a58e526805bd9abea0_***_Chenggui Yuan |
author |
Chenggui Yuan |
author2 |
Qiutong Zhu Chunfang Chen Chenggui Yuan |
format |
Journal article |
container_title |
Qualitative Theory of Dynamical Systems |
container_volume |
22 |
container_issue |
4 |
publishDate |
2023 |
institution |
Swansea University |
issn |
1575-5460 1662-3592 |
doi_str_mv |
10.1007/s12346-023-00835-7 |
publisher |
Springer Science and Business Media LLC |
college_str |
Faculty of Science and Engineering |
hierarchytype |
|
hierarchy_top_id |
facultyofscienceandengineering |
hierarchy_top_title |
Faculty of Science and Engineering |
hierarchy_parent_id |
facultyofscienceandengineering |
hierarchy_parent_title |
Faculty of Science and Engineering |
department_str |
School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics |
url |
http://dx.doi.org/10.1007/s12346-023-00835-7 |
document_store_str |
0 |
active_str |
0 |
description |
In this paper, we study the following Schrödinger–Bopp–Podolsky system: {-Δu+λV(x)u+q2φu=f(u)-Δφ+a2Δ2φ=4πu2, where u, φ: R3→ R , a>0,q>0 , λ is real positive parameter, f satisfies supper 2 lines growth. V∈ C(R3, R) , which suppose that V(x) repersents a potential well with the bottom V- 1(0) . There are no results of solutions for the system with steep potential well in the current literature because of the presence of the nonlocal term. Throughout the truncation technique and the parameter-dependent compactness lemma, we get a poistive energy solution uλ,q for λ large and q small. In the last part, we explore the asymptotic behavior as q→ 0 , λ→ + ∞ . |
published_date |
2023-12-31T14:47:24Z |
_version_ |
1776839761448665088 |
score |
11.016235 |