Nonexistence of positive supersolutions to a class of semilinear elliptic equations and systems in an exterior domain

In this paper, we consider the following semilinear elliptic equation:{-Delta u=h(x,u)in omega,u > 0on partial differential omega,where omega is an exterior domain in Double-struck capital R(N)withN > 3,h: omega x Double-struck capital R+-> Double-struck capital R is a measurable function, and derive optimal nonexistence results of positive supersolutions. Our argument is based on a nonexistence result of positive supersolutions of a linear elliptic problem with Hardy potential. We also establish sharp nonexistence results of positive supersolutions to an elliptic system.