Liouville type theorems for elliptic systems involving gradient terms

The objective of this work is to obtain Liouville type theorems for positive supersolutions of the elliptic system{−Δu+|∇u|=λvp,−Δv+|∇v|=μus, in exterior domains of RN, where p,s>0 and λ,μ>0 are parameters. We prove that positive supersolutions do not exist in some ranges of the parameters which turn out to be optimal.