The critical Schrödinger–Poisson system involving ( p , q )-Laplacian on the Heisenberg group

Abstract This paper is committed to the existence of multiple solutions for the critical Schrödinger–Poisson system involving ( p , q )-Laplacian on the Heisenberg group: − Δ H , p u − Δ H , q u + ϕ | u | p − 2 u = β | u | r − 2 u + μ ∫ Ω | u ( η ) | p λ * | η − 1 ξ | λ d η | u | p λ * − 2 u in Ω , − Δ H ϕ