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  • On ▫$p$▫-Laplacian Kirchhoff-Schrödinger-Poisson type systems with critical growth on the Heisenberg group [Elektronski vir]
    Bai, Shujie ; Song, Yueqiang ; Repovš, Dušan, 1954-
    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).
    Source: Electronic research archive. - ISSN 2688-1594 (Vol. 31, no. 9, 2023, str. 5749-5765)
    Type of material - e-article ; adult, serious
    Publish date - 2023
    Language - english
    COBISS.SI-ID - 163051011

    Link(s):

    http://www.aimspress.com/article/doi/10.3934/era.2023292
    Repository of the University of Ljubljana – RUL
    DOI

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