Liouville type theorems for systems of elliptic differential inequalities on Riemannian manifolds

In this paper we deal with the uniqueness of nonnegative solutions to systems of quasilinear elliptic differential inequalities on Riemannian manifolds, and we obtain the Liouville type theorems only in terms of the volume growth of geodesic ball. By applying the perturbation and gluing techniques, a counterexample is constructed to show the sharpness of the volume growth condition.