20.500.12556/RUL-149116 On $p$-Laplacian Kirchhoff-Schrödinger-Poisson type systems with critical growth on the Heisenberg group 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). Kirchhoff-Schrödinger-Poisson systems Heisenberg groups p-Laplacian operators critical growth concentration-compactness principle true false true Angleški jezik Ni določen Članek v reviji 2023-09-04 07:03:18 2023-09-04 07:03:22 2023-09-05 11:56:22 0000-00-00 00:00:00 2023 0 0 Str. 5749-5765 iss. 9 Vol. 31 2023 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.956.2 2688-1594 10.3934/era.2023292 163051011 RAZ_Bai_Shujie_2023.pdf RAZ_Bai_Shujie_2023.pdf 1 4EDF74ACB8E05BFDB5F5E96C24536D6C c6b1af9195441a4e62709050a4adcd476e2bb5504e94163a1bb95574ef692a1b 32a2a7e2-4ae1-11ee-af86-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=173504 http://www.aimspress.com/article/doi/10.3934/era.2023292 1 5d360f89-4ae0-11ee-af86-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=173503 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0