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

Abstract

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