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.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2009
- DOI:
- 10.48550/arXiv.0904.2072
- arXiv:
- arXiv:0904.2072
- Bibcode:
- 2009arXiv0904.2072B
- Keywords:
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- Mathematics - Analysis of PDEs;
- 35J60;
- 35J70;
- 31B25
- E-Print:
- 19 pages, 1 figure. Updated references and corrected typos