Least-energy nodal solutions of critical Schrodinger-Poisson system on the Heisenberg group

In this paper, we study the existence of least-energy nodal (sign-changing) solutions for a class of critical Schrodinger-Poisson system on the Heisenberg group given by {-Delta(H)u + mu phi vertical bar u vertical bar(q-2)u = lambda f(xi, u) + vertical bar u vertical bar(2)u, in Omega, -Delta(H)phi = vertical bar u vertical bar(q), in Omega, u = phi = 0, on partial derivative Omega, where Delta(H) is the Kohn-Laplacian on the first Heisenberg group H-1, and Omega subset of H-1 is a smooth bounded domain, lambda > 0 and mu is an element of R are some real parameters. Under the suitable conditions on f, together with the constraint variational method and the quantitative deformation lemma, we obtain the existence, energy estimates and the convergence property of the least energy sign-changing solution. However, there are several difficulties arising in the framework of Heisenberg groups, also due to the presence of the non-local coefficient as well as critical nonlinearities.