Asymptotic behavior of positive solutions of a semilinear Dirichlet problem in exterior domains

Abstract

In this article, we study the existence, uniqueness and the asymptotic behavior of a positive classical solution to the semilinear boundary-value problem -∆u = α(x)uσ in D, u|∂D = 0, lim|x|→∞ u(x) = 0. Here D is an unbounded regular domain in ℝn (n ≥ 3) with compact boundary, σ < 1 and the function α is a nonnegative function in C γ loc (D), 0 < γ < 1, satisfying an appropriate assumption related to Karamata regular variation theory.