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Existence and multiplicity of solutions for critical Kirchhoff-Choquard equations involving the fractional $p$-Laplacian on the Heisenberg group
ID
Bai, Shujie
(
Author
),
ID
Song, Yueqiang
(
Author
),
ID
Repovš, Dušan
(
Author
)
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https://jnva.biemdas.com/archives/2197
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Abstract
In this paper, we study existence and multiplicity of solutions for the following Kirchhoff-Choquard type equation involving the fractional $p$-Laplacian on the Heisenberg group: $M(\|u\|_\mu^{p})(\mu(-\Delta)^{s}_{p}u+V(\xi)|u|^{p-2}u)= f(\xi,u)+\int_{\mathbb{H}^N}\frac{|u(\eta)|^{Q_\lambda^{\ast}}}{|\eta^{-1}\xi|^\lambda}d\eta|u|^{Q_\lambda^{\ast}-2}u$ in $\mathbb{H}^N$, where $(-\Delta)^{s}_{p}$ is the fractional $p$-Laplacian on the Heisenberg group $\mathbb{H}^N$, $M$ is the Kirchhoff function, $V(\xi)$ is the potential function, $0 < s < 1$, $1 < p < \frac{N}{s}$, $\mu > 0$, $f(\xi,u)$ is the nonlinear function, $0 < \lambda < Q$, $Q=2N+2$, and $Q_\lambda^{\ast}=\frac{2Q-\lambda}{Q-2}$ is the Sobolev critical exponent. Using the Krasnoselskii genus theorem, the existence of infinitely many solutions is obtained if $\mu$ is sufficiently large. In addition, using the fractional version of the concentrated compactness principle, we prove that problem has $m$ pairs of solutions if $\mu$ is sufficiently small. As far as we know, the results of our study are new even in the Euclidean case.
Language:
English
Keywords:
fractional concentration-compactness principle
,
Krasnoselskii genus
,
Kirchhoff-Choquard type equations
,
Heisenberg group
Work type:
Article
Typology:
1.01 - Original Scientific Article
Organization:
PEF - Faculty of Education
FMF - Faculty of Mathematics and Physics
Publication status:
Published
Publication version:
Author Accepted Manuscript
Year:
2024
Number of pages:
Str. 143-166
Numbering:
Vol. 8, no. 1
PID:
20.500.12556/RUL-154014
UDC:
517.9
ISSN on article:
2560-6778
DOI:
10.23952/jnva.8.2024.1.08
COBISS.SI-ID:
181483523
Copyright:
Za shranitev recenziranega rokopisa v Repozitorij Univerze v Ljubljani je bilo pridobljeno založnikovo dovoljenje. (Datum opombe: 19. 1. 2024)
Publication date in RUL:
19.01.2024
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775
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Record is a part of a journal
Title:
Journal of nonlinear and variational analysis
Shortened title:
J. nonlinear var. anal.
Publisher:
Biemdas
ISSN:
2560-6778
COBISS.SI-ID:
18657625
Projects
Funder:
Other - Other funder or multiple funders
Funding programme:
Natural Science Foundation of Jilin Province
Project number:
222614JC010793935
Funder:
Other - Other funder or multiple funders
Funding programme:
National Natural Science Foundation of China
Project number:
12001061
Funder:
Other - Other funder or multiple funders
Funding programme:
Jilin Province, Department of Education, Research Foundation
Project number:
JJKH20220822KJ
Funder:
Other - Other funder or multiple funders
Funding programme:
Jilin Province, Innovation and Entrepreneurship Talent Funding
Project number:
2023QN21
Funder:
ARRS - Slovenian Research Agency
Project number:
P1-0292
Name:
Topologija in njena uporaba
Funder:
ARRS - Slovenian Research Agency
Project number:
J1-4031
Name:
Računalniška knjižnica za zavozlane strukture in aplikacije
Funder:
ARRS - Slovenian Research Agency
Project number:
J1-4001
Name:
Izbrani problemi iz uporabne in računske topologije
Funder:
ARRS - Slovenian Research Agency
Project number:
N1-0278
Name:
Biološka koda vozlov - identifikacija vzorcev vozlanja v biomolekulah z uporabo umetne inteligence
Funder:
ARRS - Slovenian Research Agency
Project number:
N1-0114
Name:
Algebrajski odtisi geometrijskih značilnosti v homologiji
Funder:
ARRS - Slovenian Research Agency
Project number:
N1-0083
Name:
Forsing, fuzija in kombinatorika odprtih pokritij
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