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LI, Q. RADULESCU, V. ZHANG, W.
Original Title
Normalized ground states for the Sobolev critical Schrödinger equation with at least mass critical growth
Type
journal article in Web of Science
Language
English
Original Abstract
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.
Keywords
normalized ground states; Pohozaev manifold; profile decomposition; Sobolev critical exponent
Authors
LI, Q.; RADULESCU, V.; ZHANG, W.
Released
18. 1. 2024
ISBN
0951-7715
Periodical
NONLINEARITY
Year of study
37
Number
025018
State
United Kingdom of Great Britain and Northern Ireland
Pages from
1
Pages to
29
Pages count
URL
https://iopscience-iop-org.ezproxy.lib.vutbr.cz/article/10.1088/1361-6544/ad1b8b/pdf
BibTex
@article{BUT188256, author="Quanqing {Li} and Vicentiu {Radulescu} and Wen {Zhang}", title="Normalized ground states for the Sobolev critical Schrödinger equation with at least mass critical growth", journal="NONLINEARITY", year="2024", volume="37", number="025018", pages="29", doi="10.1088/1361-6544/ad1b8b", issn="0951-7715", url="https://iopscience-iop-org.ezproxy.lib.vutbr.cz/article/10.1088/1361-6544/ad1b8b/pdf" }