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

Abstract

We obtain a Dini type blow-up condition for solutions of the differential inequality $\sum _{\left|a\right|=m}{\partial }^{\alpha }{a}_{\alpha }(x,u)\ge g\left(\left|u\right|\right) in {\mathrm{ℝ}}^n$

where $m,n\ge 1$ are integers and $a_{\alpha }$ and $g$ are some functions.