Nonexistence results for elliptic differential inequalities with a   potential on Riemannian manifolds
  In this paper we are concerned with a class of elliptic differential inequalities with a potential both on $\erre^m$ and on Riemannian manifolds. In particular, we investigate the effect of the geometry of the underlying manifold and of the behavior of the potential at infinity on nonexistence of nonnegative solutions. 
P. Mastrolia, D.D. Monticelli, F. Punzo
math.AP math.DG