On Positive Supersolutions of Fractional Elliptic Equations with Gradient Terms

In this paper,we first prove the nonexistence of positive supersolutions of the fractional elliptic equation involving the gradient term (− )su + b · ∇u = u p in the whole space RN , where p ∈ R, 0 s 1, N 2s and b is a vector field satisfying some growth condition at infinity. From this result and some reduction arguments, we then establish the nonexistence of positive supersolutions of the system (− )su + b · ∇u = v p in RN (− )sv + b · ∇v = uq in RN , where p, q ∈ R.