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Bibliographic Details
Main Authors: He, Huiting, Liu, Chungen, Zuo, Jiabin
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2407.15495
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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