A class of quasilinear differential inequalities whose solutions are ultimately constant (Q1102464)

The author studies the differential inequality \[ (Tu)(sign u) \geq f(| u|,| \text{grad} u|)\text{ on } \Omega, \] where T is a quasilinear elliptic operator, \(\Omega\) has a complement compact in \({\mathbb{R}}^ n \)and f is such that the ordinary differential equation \(y''=f(y,y')\), \(y(0)=y'(0)=0\) does not have a unique solution. He proves that u is constant for large \(| x|\) and, under mild supplementary hypothesis, u has compact support.