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

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