On a Dini type blow-up condition for solutions of higher order nonlinear differential inequalities

We obtain a Dini type blow-up condition for solutions of the differential inequality
$$ \sum_{|\alpha|=m}\partial^\alpha a_\alpha(x,u)\geq g(|u|) \quad\text{in}\quad\mathbb R^n, $$
where $m,n\geq1$ – are integers and $a_\alpha$ and $g$ – are some functions.