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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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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 This link opens in a new window
UDC:517.9
ISSN on article:2560-6778
DOI:10.23952/jnva.8.2024.1.08 This link opens in a new window
COBISS.SI-ID:181483523 This link opens in a new window
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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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 This link opens in a new window

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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