Large Solutions to Semilinear Elliptic Equations with Hardy Potential and Exponential Nonlinearity

Abstract

On a bounded smooth domain we study solutions of a semilinear elliptic equation with an exponential nonlinearity and a Hardy potential depending on the distance to the boundary of the domain. We derive global a priori bounds of the Keller-Osserman type. Using a Phragmen-Lindelof alternative for generalized sub and super-harmonic functions we discuss existence, nonexistence and uniqueness of so-called large solutions, i.e., solutions which tend to infinity at the boundary. The approach develops the one used by the same authors for a problem with a power nonlinearity instead of the exponential nonlinearity.