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: {−Δu=h(x,u)inΩ,u⩾0on∂Ω, where Ω is an exterior domain in ℝ^N with N ⩾ 3, h: Ω × ℝ⁺ → 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.