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arXiv · 0904.2072

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

Catherine Bandle·Vitaly Moroz·Wolfgang Reichel
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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.

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Catherine Bandle, Vitaly Moroz, Wolfgang Reichel. 2009-04-14. Large solutions to semilinear elliptic equations with Hardy potential and exponential nonlinearity. https://doi.org/10.1007/978-1-4419-1343-2_1

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