  We consider the inequality $$
  - \operatorname{div} A (x, \nabla u)
  \ge
  f (u)
  \quad
  \mbox{in } {\mathbb R}^n, $$ where $n \ge 2$ and $A$ is a Caratheodory
function such that $$
  C_1
  |\xi|^p
  \le
  \xi
  A (x, \xi)
  \quad
  \mbox{and}
  \quad
  |A (x, \xi)|
  \le
  C_2
  |\xi|^{p-1} $$ with some constants $C_1 > 0$, $C_2 > 0$, and $p > 1$ for
almost all $x \in {\mathbb R}^n$ and for all $\xi \in {\mathbb R}^n$. Our aim
is to find exact conditions on the function $f$ guaranteeing that any
non-negative solution of this inequality is identically zero.
