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

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

Povzetek

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).

Ključne besede

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

Podatki

Jezik:	Angleški jezik
Leto izida:	2023
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UL PEF - Pedagoška fakulteta
UDK:	517.956.2
COBISS:	163051011
ISSN:	2688-1594
Št. ogledov:	27
Št. prenosov:	5
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Vrsta dela (COBISS):	Članek v reviji
Strani:	str. 5749-5765
Letnik:	ǂVol. ǂ31
Zvezek:	ǂno. ǂ9
Čas izdaje:	2023
DOI:	10.3934/era.2023292
ID:	19888173