Nonexistence results for elliptic equations with gradient terms

We consider the elliptic problem −Δu+|∇u|q=λf(u)−Δu+|∇u|q=λf(u) in exterior domains of RNRN. Here q>1q>1, f   is a nondecreasing, continuous and positive nonlinearity defined in (0,+∞)(0,+∞) and λ>0λ>0 is a parameter. Under suitable assumptions on f near zero or infinity, we obtain some nonexistence results for positive supersolutions, depending on the relative values of q   and NN−1 and on the parameter λ.