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- W4386080964 abstract "In this article, we investigate the Kirchhoff-Schr{o}dinger-Poisson type systems on the Heisenberg group of the following form: begin{equation*} left{ begin{array}{lll} {-(a+bint_{Omega}|nabla_{H} u|^{p}dxi)Delta_{H,p}u-muphi |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} partialOmega, end{array} right. end{equation*} where $a,b$ are positive real numbers, $Omegasubset mathbb{H}^N$ is a bounded region with smooth boundary, $1<p<Q$, $Q = 2N + 2$ is the homogeneous dimension of the Heisenberg group $mathbb{H}^N$, $Q^{ast}=frac{pQ}{Q-p}$, $qin(2p, Q^{ast})$, 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)." @default.
- W4386080964 created "2023-08-23" @default.
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- W4386080964 date "2023-08-19" @default.
- W4386080964 modified "2023-09-27" @default.
- W4386080964 title "On $p$-Laplacian Kirchhoff-Schr{o}dinger-Poisson type systems with critical growth on the Heisenberg group" @default.
- W4386080964 doi "https://doi.org/10.3934/era.2023292" @default.
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