Abstract
On a bounded smooth domain Ω ⊂ ℝN, we study solutions of a semilinear elliptic equation with an exponential nonlinearity and a Hardy potential depending on the distance to ∂ ⊂. We derive global a priori bounds of the Keller-Osserman type. Using a Phragmen-Lindelöf alternative for generalize sub- and super-harmonic functions, we discuss the existence, nonexistence, and uniqueness of so-called large solutions, i.e., solutions which tend to infinity at ∂ ⊂. 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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Bandle, C., Moroz, V., Reichel, W. (2010). Large Solutions to Semilinear Elliptic Equations with Hardy Potential and Exponential Nonlinearity. In: Laptev, A. (eds) Around the Research of Vladimir Maz'ya II. International Mathematical Series, vol 12. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1343-2_1
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DOI: https://doi.org/10.1007/978-1-4419-1343-2_1
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