On the existence of global solutions of second-order quasilinear elliptic inequalities
We study the existence of global positive solutions of the differential inequalities $$ - \operatorname{div} A (x, u, \nabla u) \ge f (u) \quad \mbox{in } {\mathbb R}^n, $$ where $n \ge 2$ and $A$ is a Carathéodory function such that $$ (A (x, s, ζ) - A (x, s, ξ))(ζ- ξ) \ge 0, $$ $$ C_1 |ξ|^p \le ξ A (x, s, ξ), \quad |A (x, s, ξ)| \le C_2 |ξ|^{p-1}, \quad C_1, C_2 > 0, \; p > 1, $$ for almost all $x \in {\mathbb R}^n$ and for all $s \in {\mathbb R}$ and $ζ, ξ\in {\mathbb R}^n$.
math.AP↗