Large solutions to semilinear elliptic equations with Hardy potential and exponential nonlinearity

Details Large solutions to semilinear elliptic equations with Hardy potential and exponential nonlinearity Large solutions to semilinear elliptic equations with Hardy potential and exponential nonlinearity

2009-04-14

arxiv.org/abs/0904.2072v2

Mathematics

Analysis of PDEs

19 pages, 1 figure. Updated references and corrected typos

Scientific paper

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.

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