Liouville type theorems for two elliptic equations with advections
Anh Tuan Duong, Nguyen Nhu Thang, Thi Quynh Nguyen · Annales Polonici Mathematici · 2019
We study the elliptic equations $$ -\Delta u+a(x)\cdot abla u=f(u)\ \quad\mbox{in }\mathbb R^{N}, $$ where $ N\geq 3 $, the advection term $a(x)$ is a smooth vector field satisfying a certain decay condition and the nonlinearity $f(u)$ is of the form $-u