LAUSR

Abstract Let H n be the Heisenberg group, Q = 2 n + 2 be the homogeneous dimension of H n , we study the existence of solutions for the following Q-Laplacian elliptic system { − K ( ∫ Ω | ∇ H n u | Q d ξ ) Δ Q u = λ G u ( ξ , u , v ) ρ ( ξ ) ℘ in Ω ; − K ( ∫ Ω | ∇ H n v | Q d ξ ) Δ Q v = λ G v ( ξ , u , v ) ρ ( ξ ) ℘ in Ω ; u = 0 , v = 0 , on ∂ Ω , where Ω is an open, smooth and bounded subset of Heisenberg group H n , K is a Kirchhoff type function, 0 ≤ ℘ Q and λ is a positive parameter, and nonlinear terms G u , G v have critical exponential growth behave like exp ⁡ ( β | s | Q Q − 1 ) as | s | → + ∞ with some β > 0 .