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

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

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).

• Jezik: Angleški jezik
• Ključne besede: Kirchhoff-Schrödinger-Poisson systems, Heisenberg groups, p-Laplacian operators, critical growth, concentration-compactness principle
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: PEF - Pedagoška fakulteta; FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2023
• Št. strani: Str. 5749-5765
• Številčenje: Vol. 31, iss. 9
• PID: 20.500.12556/RUL-149116
• UDK: 517.956.2
• ISSN pri članku: 2688-1594
• DOI: 10.3934/era.2023292
• COBISS.SI-ID: 163051011
• Datum objave v RUL: 04.09.2023

Gradivo je del revije

• Naslov: Electronic research archive
• Skrajšan naslov: Electron. res. arch.
• Založnik: American institute of mathematical sciences
• ISSN: 2688-1594
• COBISS.SI-ID: 20165635

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.