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Schrödinger–Bopp–Podolsky System with Steep Potential Well

Qiutong Zhu, Chunfang Chen, Chenggui Yuan Orcid Logo

Qualitative Theory of Dynamical Systems, Volume: 22, Issue: 4

Swansea University Author: Chenggui Yuan Orcid Logo

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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)...

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Published in: Qualitative Theory of Dynamical Systems
ISSN: 1575-5460 1662-3592
Published: Springer Science and Business Media LLC 2023
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URI: https://cronfa.swan.ac.uk/Record/cronfa64044
first_indexed 2023-08-08T10:17:05Z
last_indexed 2024-11-25T14:13:20Z
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spelling 2024-09-04T16:55:12.0634016 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 MACS 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 and Computer Science School COLLEGE CODE MACS 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). 2024-09-04T16:55:12.0634016 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 64044__28415__12d69e04878d4e758229910c7ce8cac6.pdf 64044.pdf 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 1
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 2023-12-31T05:15:15Z
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score 11.096892

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