  In this article we present a simple and unified probabilistic approach to
prove nonexistence of positive super-solutions for systems of equations
involving potential terms and the fractional Laplacian in an exterior domain.
Such problems arise in the analysis of a priori estimates of solutions. The
class of problems we consider in this article is quite general compared to the
literature. The main ingredient for our proofs is the hitting time estimates
for the symmetric $\alpha$-stable process and probabilistic representation of
the super-solutions.
