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

IF 1 4区 数学 Q1 MATHEMATICS
Shujie Bai, Yueqiang Song, Dušan D. Repovš
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引用次数: 0

Abstract

In this article, we investigate the Kirchhoff-Schrödinger-Poisson type systems on the Heisenberg group of the following form: \begin{document}$ \begin{equation*} \left\{ \begin{array}{lll} {-(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{array} \right. \end{equation*} $\end{document} 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 $, we establish existence and multiplicity results for the system above. To some extent, we generalize the results of An and Liu (Israel J. Math., 2020) and Liu et al. (Adv. Nonlinear Anal., 2022).
关于Heisenberg群上具有临界增长的$p$-Laplaccian-Kirchhoff-Schrödinger-Poisson型系统
在这篇文章中,我们研究了以下形式的海森堡群上的Kirchhoff-Schrödinger-Poisson型系统:\beart{document}$\beart}方程*}\left\{\bearth{array}{lll}{-(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和\ mbox{in}\\Omega,\\-\Delta_{H}\phi=| u | ^{p}和\ mbox{in}\\ Omega,\\ u=\ phi=0&\ mbox{on}\\ partial \ Omega,\ end{array}\ right。\end{equation*}$\end{document}其中$a,b$是正实数,$\Omega\subet\mathbb{H}^N$是具有光滑边界的有界区域,$1
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来源期刊
CiteScore
1.30
自引率
12.50%
发文量
170
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