On blow-up conditions for solutions of higher order differential inequalities

Abstract

For differential inequalities of the form $$ \sum_{|α| = m} (- 1)^m \partial^α a_α(x, u) \ge b (x) |u|^λ \quad \mbox{in } {\mathbb R}^n, \: n \ge 1, $$ where $a_{\alpha }$ and $b$ are some functions, we obtain conditions guaranteeing that any solution is identically equal to zero. We construct examples which show that the obtained conditions are sharp.