  We obtain a Dini type blow-up condition for global weak solutions of the
differential inequality $$
  \sum_{|\alpha| = m}
  \partial^\alpha
  a_\alpha (x, u)
  \ge
  g (|u|)
  \quad
  \mbox{in } {\mathbb R}^n, $$ where $m, n \ge 1$ are integers and $a_\alpha$
and $g$ are some functions.
