Constraint minimizers of mass critical fractional Kirchhoff equations: concentration and uniqueness

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F25%3APU156196" target="_blank" >RIV/00216305:26220/25:PU156196 - isvavai.cz</a>

Result on the web

<a href="https://iopscience-iop-org.ezproxy.lib.vutbr.cz/article/10.1088/1361-6544/adbc3b/pdf" target="_blank" >https://iopscience-iop-org.ezproxy.lib.vutbr.cz/article/10.1088/1361-6544/adbc3b/pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1361-6544/adbc3b" target="_blank" >10.1088/1361-6544/adbc3b</a>

Result language

angličtina

Original language name

Constraint minimizers of mass critical fractional Kirchhoff equations: concentration and uniqueness

Original language description

This paper focuses on the constraint minimization problem associated with the fractional Kirchhoff equation { ( a + b ∫ ℝ N | ( − Δ ) s 2 u | 2 d x ) ( − Δ ) s u + | x | 2 u = μ u + β u 8 s N + 1 in ℝ N , [ 6 p t ] ∫ ℝ N | u | 2 d x = 1 , where s ∈ ( N / 4 , 1 ) , N = 2 , 3 , a ⩾ 0 , b > 0 are constants, μ ∈ R is the corresponding Lagrange multiplier and ( − Δ ) s is the fractional Laplacian operator, 8 s / N + 1 is the corresponding mass critical exponent. The purpose of this paper is threefold: to establish the existence and non-existence of the L2-constraint minimizers to the degenerate fractional Kirchhoff problem, that is a = 0, to prove some classical concentration behaviors of constraint minimizers and to reveal the local uniqueness of constraint minimizers of above problem under double nonlocal effect. In particular, we will give some energy estimates, decay estimates and uniform regularity to find that the maximal point of constraint minimizer concentrates on the bottom point of the homogeneous potential. Furthermore, we introduce several new techniques based on the combination of the localization method of ( − Δ ) s and by establishing the nonlocal Pohozăev identity, which allow us to get over some new challenges due to the nonlocal property of ( − Δ ) s and the fact that ∫ R N | ( − Δ ) s 2 u | 2 d x ( − Δ ) s u does not vanish as a ↘ 0 . We believe that these techniques will have some potential applications in various related problems.

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

2025

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

38

Issue of the periodical within the volume

4

Country of publishing house

GB - UNITED KINGDOM

Number of pages

46

Pages from-to

„“-„“

UT code for WoS article

001443870900001

EID of the result in the Scopus database

2-s2.0-105000363566