Existence of a positive solution for a singular elliptic problem with general exponential growth

Abstract

We prove the existence of a positive solution for a singular elliptic equation with singular boundary condition. The nonlinearity considered in the equation and on the boundary involve the Trudinger–Moser growth which can be subcritical, critical or supercritical. We use an approximation scheme together with Brouwer’s theorem to establish the existence of a positive solution.