Large Solutions to Semilinear Elliptic Equations with Hardy Potential and Exponential Nonlinearity

  • Catherine Bandle
  • Vitaly Moroz
  • Wolfgang Reichel
Part of the International Mathematical Series book series (IMAT, volume 12)


On a bounded smooth domain Ω ⊂ ℝ N , 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.


Comparison Principle Hardy Inequality Large Solution Nonexistence Result Bounded Smooth Domain 
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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Catherine Bandle
    • 1
  • Vitaly Moroz
    • 2
  • Wolfgang Reichel
    • 3
  1. 1.Mathematisches InstitutUniversität BaselBaselSwitzerland
  2. 2.Department of MathematicsSwansea UniversitySwanseaUK
  3. 3.Fakultät für MathematikUniversität Karlsruhe (TH)KarlsruheGermany

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