Positive Solutions of Singular Elliptic Equations Outside the Unit Disk

Abstract

We study the existence and the asymptotic behaviour of positive solutions for the nonlinear singular elliptical equation Δu + φ (., u) = 0 in the outside of the unit disk in ℝ2, with homogeneous Dirichlet boundary condition. The aim is to prove some existence results for the above equation in a general setting by using a potential theory approach.