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

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

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).

• Language: English
• Keywords: Kirchhoff-Schrödinger-Poisson systems, Heisenberg groups, p-Laplacian operators, critical growth, concentration-compactness principle
• 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: Version of Record
• Year: 2023
• Number of pages: Str. 5749-5765
• Numbering: Vol. 31, iss. 9
• PID: 20.500.12556/RUL-149116
• UDC: 517.956.2
• ISSN on article: 2688-1594
• DOI: 10.3934/era.2023292
• COBISS.SI-ID: 163051011
• Publication date in RUL: 04.09.2023

Record is a part of a journal

• Title: Electronic research archive
• Shortened title: Electron. res. arch.
• Publisher: American institute of mathematical sciences
• ISSN: 2688-1594
• COBISS.SI-ID: 20165635

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• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
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