On p-Laplacian Kirchhoff-Schrödinger-Poisson type systems with critical growth on the Heisenberg group

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

Abstract

In this article, we investigate the Kirchhoff-Schrödinger-Poisson type systems on the Heisenberg group of the following form: ▫$\begin{cases} {-(a+b\int_{\Omega}|\nabla_{H} u|^{p}d\xi)\Delta_{H, p}u-\mu\phi |u|^{p-2}u} = \lambda |u|^{q-2}u+|u|^{Q^{\ast}-2}u & \mbox{in}\ \Omega, \\ -\Delta_{H}\phi = |u|^{p} & \mbox{in}\ \Omega, \\ u = \phi = 0 & \mbox{on}\ \partial\Omega, \end{cases}$▫ where ▫$a, b$▫ are positive real numbers, ▫$\Omega\subset \mathbb{H}^N$▫ is a bounded region with smooth boundary, ▫$1 < p < Q$▫, ▫$Q = 2N + 2$▫ is the homogeneous dimension of the Heisenberg group ▫$\mathbb{H}^N$▫, ▫$Q^{\ast} = \frac{pQ}{Q-p}$▫, ▫$q\in(2p, Q^{\ast})$▫ and ▫$\Delta_{H, p}u = \mbox{div}(|\nabla_{H} u|^{p-2}\nabla_{H} u)$▫ is the ▫$p$▫-horizontal Laplacian. Under some appropriate conditions for the parameters ▫$\mu$▫ and ▫$\lambda$▫, we establish existence and multiplicity results for the system above. To some extent, we generalize the results of An and Liu (Israel J. Math., 2020) and Liu et al. (Adv. Nonlinear Anal., 2022).

Keywords

Kirchhoff-Schrödinger-Poisson systems;Heisenberg groups;p-Laplacian operators;critical growth;concentration-compactness principle;

Data

Language:	English
Year of publishing:	2023
Typology:	1.01 - Original Scientific Article
Organization:	UL PEF - Faculty of Education
UDC:	517.956.2
COBISS:	163051011
ISSN:	2688-1594
Views:	27
Downloads:	5
Average score:	0 (0 votes)
Metadata:

Other data

Type (COBISS):	Article
Pages:	str. 5749-5765
Volume:	ǂVol. ǂ31
Issue:	ǂno. ǂ9
Chronology:	2023
DOI:	10.3934/era.2023292
ID:	19888173