On global solutions of quasilinear second-order elliptic inequalities

A. A. Kon'kov, A. E. Shishkov

Published 2024-01-13Version 1

For non-negative solutions of the inequality $$ - \operatorname{div} (|\nabla u|^{p-2} \nabla u) \ge f (u) \quad \mbox{in } {\mathbb R}^n, $$ where $n \ge 2$ is an integer and $p > 1$ is a real number, we obtain necessary and sufficient blow-up conditions.