Nonexistence results for elliptic differential inequalities with a   potential in bounded domains
  In this paper we are concerned with a class of elliptic differential inequalities with a potential in bounded domains both of $\mathbf{R}^m$ and of Riemannian manifolds. In particular, we investigate the effect of the behavior of the potential at the boundary of the domain on nonexistence of nonnegative solutions. 
Dario D. Monticelli and Fabio Punzo
math.AP math.DG