Abstract

We study the elliptic equations −Δu+a(x)⋅∇u=f(u) in RN, where N≥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−p,p>0, or eu. We establish Liouville type theorems for the class of positive stable solutions when f(u)=−u−p and for the class of stable solutions when f(u)=eu. In particular, our results improve some results of B. Lai and L. Zhang [Z. Anal. Anwend. 36 (2017), 283–295] and of L. Ma and J. C. Wei [J. Funct. Anal. 254 (2008), 1058–1087].