Existence of solutions for Kirchhoff type systems involving Q-Laplacian operator in Heisenberg group

Let H-n be the Heisenberg group, Q = 2n + 2be the homogeneous dimension of H-n, we study the existence of solutions for the following Q-Laplacian elliptic system {-K(integral(Omega)vertical bar del(Hn)u vertical bar(Q)d xi)Delta(Q)u = lambda Gu(xi,u,v/(xi)(&) in Omega; -K(integral(Omega)vertical bar del(Hn)v vertical bar(Q)d xi)Delta(Q)v = lambda Gv(xi,u,v/(xi)(&) in Omega; u = 0, v = 0, on partial derivative Omega, where Omega is an open, smooth and bounded subset of Heisenberg group H-n, K is a Kirchhoff type function, 0 <= P < Qand lambda is a positive parameter, and nonlinear terms G(u), G(v) have critical exponential growth behave like exp(beta vertical bar s vertical bar(Q/Q-1)) as vertical bar s vertical bar -> +infinity with some beta > 0. (C) 2020 Elsevier Inc. All rights reserved.