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 R n ( n ≥ 3 ), where A ( x ) is bounded and uniformly elliptic, b ( x ) = O ( | x | − 1 ) , div b = 0 and f is a continuous and positive function in ( 0 , ∞ ) satisfying f ( u ) ∼ u q as u → 0 with q ≤ n / ( n − 2 ) . Furthermore, we investigate general conditions on b and f for nonexistence of positive supersolutions. [ABSTRACT FROM AUTHOR]