Liouville theorems for supersolutions of semilinear elliptic equations with drift terms in exterior domains

In this paper, we prove nonexistence of positive supersolutions of a semilinear equation −div(A(x)∇u)+b(x)⋅∇u=f(u) in exterior domains in Rn (n≥3), where A(x) is bounded and uniformly elliptic, b(x)=O(|x|−1), divb=0 and f is a continuous and positive function in (0,∞) satisfying f(u)∼uq as u→0 with q≤n/(n−2). Furthermore, we investigate general conditions on b and f for nonexistence of positive supersolutions.