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Schrödinger–Bopp–Podolsky System with Steep Potential Well
Qiutong Zhu,
Chunfang Chen,
Chenggui Yuan 
Qualitative Theory of Dynamical Systems, Volume: 22, Issue: 4
Swansea University Author:
Chenggui Yuan
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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)...
| Published in: | Qualitative Theory of Dynamical Systems |
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| ISSN: | 1575-5460 1662-3592 |
| Published: |
Springer Science and Business Media LLC
2023
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa64044 |
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| 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→ + ∞ . |
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| Keywords: |
Schrödinger-Bopp-Podolsky system, Truncation technique, Parameter-dependentcompactness lemma, Asymptotic behavior |
| College: |
Faculty of Science and Engineering |
| 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). |
| Issue: |
4 |