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On the nonlocal Schr\”{o}dinger-Poisson type system in the Heisenberg group
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  • Zeyi Liu,
  • Min Zhao,
  • Deli Zhang,
  • Sihua Liang
Zeyi Liu
Changchun Normal University
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Min Zhao
Changchun Normal University
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Deli Zhang
Changchun Normal University
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Sihua Liang
Changchun Normal University
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Abstract

This paper is concerned with the following nonlocal Schr\”{o}dinger-Poisson type system: \begin{equation*} \begin{cases} -\left(a-b\int_{\Omega}|\nabla_{H}u|^{2}dx\right)\Delta_{H}u+\mu\phi u=\lambda|u|^{q-2}u, &\mbox{in} \ \Omega,\\ -\Delta_{H}\phi=u^2 & \mbox{in}\ \Omega,\\ u=\phi=0 & \mbox{on}\ \partial\Omega, \end{cases} \end{equation*} where $a, b>0$ and $\Delta_H$ is the Kohn-Laplacian on the first Heisenberg group $\mathbb{H}^1$, $\Omega\subset \mathbb{H}^1$ is a smooth bounded domain, $\lambda>0$, $\mu\in \mathbb{R}$ are some real parameters and $1“”

Peer review status:ACCEPTED

05 May 2021Submitted to Mathematical Methods in the Applied Sciences
06 May 2021Submission Checks Completed
06 May 2021Assigned to Editor
10 May 2021Reviewer(s) Assigned
05 Sep 2021Review(s) Completed, Editorial Evaluation Pending
06 Sep 2021Editorial Decision: Revise Minor
06 Sep 20211st Revision Received
06 Sep 2021Submission Checks Completed
06 Sep 2021Assigned to Editor
06 Sep 2021Reviewer(s) Assigned
08 Sep 2021Review(s) Completed, Editorial Evaluation Pending
16 Sep 2021Editorial Decision: Accept