Non-existence results for semilinear Kohn-Laplace equations in unbounded domains

In this paper we prove several non-existence theorems for the boundary value problem (formula presented) where Ωis a connected unbounded open subset of the Heisenberg group ℍn, △ℍn denotes the Kohn Laplacian on ℍn and S10 (Ω) is the Sobolev-Stein space, completion of C∞0(Ω) with respect to the norm (formula presented) ▽ℍn stands for the intrinsic gradient on Hn. We shall denote by Q:= 2n + 2 the homogeneous dimension of ℍn and by Q*:= 2Q/Q-2 the exponent of the Sobolev-type embedding.