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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.15495 |
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| _version_ | 1866916715940544512 |
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| author | He, Huiting Liu, Chungen Zuo, Jiabin |
| author_facet | He, Huiting Liu, Chungen Zuo, Jiabin |
| contents | This paper is concerned with the ground states of a coupled pseudo-relativistic Hartree system in $\mathbb{R} ^{3} $ with trapping potentials, where the intraspecies and the interspecies interaction are both attractive. By investigating an associated constraint minimization problem, the existence and non-existence of ground states are classified completely. Under certain conditions on the trapping potentials, we present a precise analysis on the concentration behavior of the minimizers as the coupling coefficient goes to a critical value, where the minimizers blow up and the maximum point sequence concentrates at a global minima of the associated trapping potentials. We also identify an optimal blowing up rate under polynomial potentials by establishing some delicate estimates of energy functionals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15495 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ground states of a coupled pseudo-relativistic Hartree system: existence and concentration behavior He, Huiting Liu, Chungen Zuo, Jiabin Analysis of PDEs 35Q40, 35B40, 35R11 This paper is concerned with the ground states of a coupled pseudo-relativistic Hartree system in $\mathbb{R} ^{3} $ with trapping potentials, where the intraspecies and the interspecies interaction are both attractive. By investigating an associated constraint minimization problem, the existence and non-existence of ground states are classified completely. Under certain conditions on the trapping potentials, we present a precise analysis on the concentration behavior of the minimizers as the coupling coefficient goes to a critical value, where the minimizers blow up and the maximum point sequence concentrates at a global minima of the associated trapping potentials. We also identify an optimal blowing up rate under polynomial potentials by establishing some delicate estimates of energy functionals. |
| title | Ground states of a coupled pseudo-relativistic Hartree system: existence and concentration behavior |
| topic | Analysis of PDEs 35Q40, 35B40, 35R11 |
| url | https://arxiv.org/abs/2407.15495 |