On removable singularities of solutions of higher order differential inequalities

Abstract

We obtain sufficient conditions for solutions of the $m$th-order differential inequality $$ \sum_{|α| = m} \partial^αa_α(x, u) \ge f (x) g (|u|) \quad \mbox{in } B_1 \setminus \{ 0 \} $$ to have a removable singularity at zero, where $a_{\alpha }$, $f$, and $g$ are some functions, and $B_1=\{x:|x|<1\}$ is a unit ball in ${\mathbb{R}}^n$. Constructed examples demonstrate the exactness of these conditions.

This paper is submitted to Advanced Nonlinear Studies