VSE knjižnice (vzajemna bibliografsko-kataložna baza podatkov COBIB.SI)
  • 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).
    Vir: Electronic research archive. - ISSN 2688-1594 (Vol. 31, no. 9, 2023, str. 5749-5765)
    Vrsta gradiva - e-članek ; neleposlovje za odrasle
    Leto - 2023
    Jezik - angleški
    COBISS.SI-ID - 163051011

    Povezava(-e):

    http://www.aimspress.com/article/doi/10.3934/era.2023292
    Repozitorij Univerze v Ljubljani – RUL
    DOI

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