Blow-up solutions with minimal mass for nonlinear Schrödinger equation with variable potential

This paper studies the mass-critical variable coefficient nonlinear Schrödinger equation. We first get the existence of the ground state by solving a minimization problem. Then we prove a compactness result by the variational characterization of the ground state solutions. In addition, we construct...

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Autores principales:	Pan Jingjing, Zhang Jian
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	variable coefficient nonlinear schrödinger equation minimal mass blow-up solutions variational characterization ground state compactness 35q55 35b44 Analysis QA299.6-433
Acceso en línea:	https://doaj.org/article/50f43f151ff94a1a846067da8b374f1b
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spelling	oai:doaj.org-article:50f43f151ff94a1a846067da8b374f1b2021-12-05T14:10:40ZBlow-up solutions with minimal mass for nonlinear Schrödinger equation with variable potential2191-94962191-950X10.1515/anona-2020-0185https://doaj.org/article/50f43f151ff94a1a846067da8b374f1b2021-06-01T00:00:00Zhttps://doi.org/10.1515/anona-2020-0185https://doaj.org/toc/2191-9496https://doaj.org/toc/2191-950XThis paper studies the mass-critical variable coefficient nonlinear Schrödinger equation. We first get the existence of the ground state by solving a minimization problem. Then we prove a compactness result by the variational characterization of the ground state solutions. In addition, we construct the blow-up solutions at the minimal mass threshold and further prove the uniqueness result on the minimal mass blow-up solutions which are pseudo-conformal transformation of the ground states.Pan JingjingZhang JianDe Gruyterarticlevariable coefficient nonlinear schrödinger equationminimal mass blow-up solutionsvariational characterizationground statecompactness35q5535b44AnalysisQA299.6-433ENAdvances in Nonlinear Analysis, Vol 11, Iss 1, Pp 58-71 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	variable coefficient nonlinear schrödinger equation minimal mass blow-up solutions variational characterization ground state compactness 35q55 35b44 Analysis QA299.6-433
spellingShingle	variable coefficient nonlinear schrödinger equation minimal mass blow-up solutions variational characterization ground state compactness 35q55 35b44 Analysis QA299.6-433 Pan Jingjing Zhang Jian Blow-up solutions with minimal mass for nonlinear Schrödinger equation with variable potential
description	This paper studies the mass-critical variable coefficient nonlinear Schrödinger equation. We first get the existence of the ground state by solving a minimization problem. Then we prove a compactness result by the variational characterization of the ground state solutions. In addition, we construct the blow-up solutions at the minimal mass threshold and further prove the uniqueness result on the minimal mass blow-up solutions which are pseudo-conformal transformation of the ground states.
format	article
author	Pan Jingjing Zhang Jian
author_facet	Pan Jingjing Zhang Jian
author_sort	Pan Jingjing
title	Blow-up solutions with minimal mass for nonlinear Schrödinger equation with variable potential
title_short	Blow-up solutions with minimal mass for nonlinear Schrödinger equation with variable potential
title_full	Blow-up solutions with minimal mass for nonlinear Schrödinger equation with variable potential
title_fullStr	Blow-up solutions with minimal mass for nonlinear Schrödinger equation with variable potential
title_full_unstemmed	Blow-up solutions with minimal mass for nonlinear Schrödinger equation with variable potential
title_sort	blow-up solutions with minimal mass for nonlinear schrödinger equation with variable potential
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/50f43f151ff94a1a846067da8b374f1b
work_keys_str_mv	AT panjingjing blowupsolutionswithminimalmassfornonlinearschrodingerequationwithvariablepotential AT zhangjian blowupsolutionswithminimalmassfornonlinearschrodingerequationwithvariablepotential
_version_	1718371840046399488

Blow-up solutions with minimal mass for nonlinear Schrödinger equation with variable potential

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