Classification of supersolutions and Liouville theorems for some nonlinear elliptic problems
Classification of supersolutions and Liouville theorems for some nonlinear elliptic problems
In this paper we consider positive supersolutions of the elliptic equation $-\triangle u =f(u) |\nabla u|^q$, posed in exterior domains of $\mathbb{R}^N$ ($N\ge 2$), where $f$ iscontinuous in $[0,+\infty)$ and positive in $(0,+\infty)$ and $q>0$. We classifysupersolutions $u$ into four types depending on the function $m(R)=\inf_{|x|=R}u(x)$ for large $R$, and …