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.

19 pages, 1 figure. Updated references and corrected typos

References in corpus (1)

• "Boundary blowup" type sub-solutions to semilinear elliptic equations with Hardy potential

Cited by in corpus (2)

• Boundary singularities of solutions of semilinear elliptic equations in the half-space with a Hardy potential
• Large solutions of semilinear equations with Hardy potential