Existence and multiplicity of solutions for critical Kirchhoff-Choquard equations involving the fractional p-Laplacian on the Heisenberg group

Shujie Bai (Author), Yueqiang Song (Author), Dušan Repovš (Author)

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.

Keywords

fractional concentration-compactness principle;Krasnoselskii genus;Kirchhoff-Choquard type equations;Heisenberg group;

Data

Language:	English
Year of publishing:	2024
Typology:	1.01 - Original Scientific Article
Organization:	UL PEF - Faculty of Education
UDC:	517.9
COBISS:	181483523
ISSN:	2560-6778
Views:	37
Downloads:	14
Average score:	0 (0 votes)
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Other data

Type (COBISS):	Article
Pages:	str. 143-166
Volume:	ǂVol. ǂ8
Issue:	ǂiss. ǂ1
Chronology:	2024
DOI:	10.23952/jnva.8.2024.1.08
ID:	22454856