Existence of positive solution for critical Schrödinger-Poisson system on the first Heisenberg group

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Abstract

In this article, we consider a class of critical Schrödinger-Poisson type systems on the first Heisenberg group. We demonstrate that the system admits a positive ground state solution by utilizing the concentration compactness principle and critical point theory. The system has double critical nonlinearity on the Heisenberg group, which is the novelty and peculiarity of this paper. To some extent, we extend some previous results.

Keywords

Heisenberg group / Schrödinger-Poisson system / concentration-compactness principle / variational methods

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