Asymptotic profile of least energy solutions to the nonlinear Schrödinger-Bopp-Podolsky system

Fuente: arXiv

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Bibliographische Detailangaben
1. Verfasser:	Ramos, Gustavo de Paula
Format:	Preprint
Veröffentlicht:	2024
Schlagworte:	Analysis of PDEs
Online-Zugang:	Acceder al recurso
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_version_	1866908415313313792
author	Ramos, Gustavo de Paula
author_facet	Ramos, Gustavo de Paula
contents	Consider the following nonlinear Schrödinger--Bopp--Podolsky system in $\mathbb{R}^3$: \[ \begin{cases} - Δv + v + ϕv = v \|v\|^{p - 2}; \\ β^2 Δ^2 ϕ- Δϕ= 4 πv^2, \end{cases} \] where $β> 0$ and $3 < p < 6$, the unknowns being $v$, $ϕ\colon \mathbb{R}^3 \to \mathbb{R}$. We prove that, as $β\to 0$ and up to translations and subsequences, least energy solutions to this system converge to a least energy solution to the following nonlinear Schrödinger--Poisson system in $\mathbb{R}^3$: \[ \begin{cases} - Δv + v + ϕv = v \|v\|^{p - 2}; \\ - Δϕ= 4 πv^2. \end{cases} \]
format	Preprint
id	arxiv_https___arxiv_org_abs_2407_19141
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Asymptotic profile of least energy solutions to the nonlinear Schrödinger-Bopp-Podolsky system Ramos, Gustavo de Paula Analysis of PDEs Consider the following nonlinear Schrödinger--Bopp--Podolsky system in $\mathbb{R}^3$: \[ \begin{cases} - Δv + v + ϕv = v \|v\|^{p - 2}; \\ β^2 Δ^2 ϕ- Δϕ= 4 πv^2, \end{cases} \] where $β> 0$ and $3 < p < 6$, the unknowns being $v$, $ϕ\colon \mathbb{R}^3 \to \mathbb{R}$. We prove that, as $β\to 0$ and up to translations and subsequences, least energy solutions to this system converge to a least energy solution to the following nonlinear Schrödinger--Poisson system in $\mathbb{R}^3$: \[ \begin{cases} - Δv + v + ϕv = v \|v\|^{p - 2}; \\ - Δϕ= 4 πv^2. \end{cases} \]
title	Asymptotic profile of least energy solutions to the nonlinear Schrödinger-Bopp-Podolsky system
topic	Analysis of PDEs
url	https://arxiv.org/abs/2407.19141