On removable singularities of solutions of higher order differential inequalities

Abstract

We obtain sufficient conditions for solutions of the $m$th-order differential inequality $$ \sum_{|\alpha| = m} \partial^\alpha a_\alpha (x, u) \ge f (x) g (|u|) \quad \mbox{in } B_1 \setminus \{ 0 \} $$ 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.