Daniel Devine

Nonexistence of positive entire solutions to systems of semilinear elliptic inequalities

Abstract Consider the system $$\begin{aligned} \left\{ \begin{aligned}&\Delta u \ge p(x)g(v) \quad & \text{ in } \mathbb {R}^n, \\&\Delta v \ge q(x)f(|\nabla u|) \quad & \text{ in } \mathbb {R}^n, \\&u>0, v>0 \quad & \text{ in } \mathbb {R}^n, \end{a...