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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2024

Confidentiality

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

Name of the periodical

NONLINEARITY

ISSN

0951-7715

e-ISSN

1361-6544

Volume of the periodical

37

Issue of the periodical within the volume

025018

Country of publishing house

GB - UNITED KINGDOM

Number of pages

29

Pages from-to

1-29

UT code for WoS article

001146574500001

EID of the result in the Scopus database

2-s2.0-85182783159