Normalized ground states for the Sobolev critical Schrödinger equation with at least mass critical growth

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F24%3APU151074" target="_blank" >RIV/00216305:26220/24:PU151074 - isvavai.cz</a>

Výsledek na webu

<a href="https://iopscience-iop-org.ezproxy.lib.vutbr.cz/article/10.1088/1361-6544/ad1b8b/pdf" target="_blank" >https://iopscience-iop-org.ezproxy.lib.vutbr.cz/article/10.1088/1361-6544/ad1b8b/pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1361-6544/ad1b8b" target="_blank" >10.1088/1361-6544/ad1b8b</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Normalized ground states for the Sobolev critical Schrödinger equation with at least mass critical growth

Popis výsledku v původním jazyce

In the present paper, we investigate the existence of ground state solutions to the Sobolev critical nonlinear Schrödinger equation − Δ u + λ u = g u + | u | 2 ∗ − 2 u in R N , ∫ R N | u | 2 d x = m 2 , where N ⩾ 3 , m > 0, 2 ∗ := 2 N N − 2 , λ is an unknown parameter that will appear as a Lagrange multiplier, g is a mass critical or supercritical but Sobolev subcritical nonlinearity. With the aid of the minimization of the energy functional over a linear combination of the Nehari and Pohozaev constraints intersected with the product of the closed balls in L 2 ( R N ) of radii m and the profile decomposition, we obtain a couple of the normalized ground state solution to ( P m ) that is independent of the sign of the Lagrange multiplier. This result complements and extends the paper by Bieganowski and Mederski (2021 J. Funct. Anal. 280 108989) concerning the above problem from the Sobolev subcritical setting to the Sobolev critical framework. We also answer an open problem that was proposed by Jeanjean and Lu (2020 Calc. Var. PDE 59 174). Furthermore, the asymptotic behavior of the ground state energy map is also studied.

Název v anglickém jazyce

Normalized ground states for the Sobolev critical Schrödinger equation with at least mass critical growth

Popis výsledku anglicky

In the present paper, we investigate the existence of ground state solutions to the Sobolev critical nonlinear Schrödinger equation − Δ u + λ u = g u + | u | 2 ∗ − 2 u in R N , ∫ R N | u | 2 d x = m 2 , where N ⩾ 3 , m > 0, 2 ∗ := 2 N N − 2 , λ is an unknown parameter that will appear as a Lagrange multiplier, g is a mass critical or supercritical but Sobolev subcritical nonlinearity. With the aid of the minimization of the energy functional over a linear combination of the Nehari and Pohozaev constraints intersected with the product of the closed balls in L 2 ( R N ) of radii m and the profile decomposition, we obtain a couple of the normalized ground state solution to ( P m ) that is independent of the sign of the Lagrange multiplier. This result complements and extends the paper by Bieganowski and Mederski (2021 J. Funct. Anal. 280 108989) concerning the above problem from the Sobolev subcritical setting to the Sobolev critical framework. We also answer an open problem that was proposed by Jeanjean and Lu (2020 Calc. Var. PDE 59 174). Furthermore, the asymptotic behavior of the ground state energy map is also studied.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

NONLINEARITY

ISSN

0951-7715

e-ISSN

1361-6544

Svazek periodika

37

Číslo periodika v rámci svazku

025018

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

29

Strana od-do

1-29

Kód UT WoS článku

001146574500001

EID výsledku v databázi Scopus

2-s2.0-85182783159