Journal d’Analyse Mathématique

, Volume 100, Issue 1, pp 249–280

Concentrating solutions for the Hénon equation in ℝ2

Article

Abstract

We consider the boundary value problem Δu+⋎xup=0, α>0, in the unit ballB with homogeneous Dirichlet boundary condition andp a large exponent. We find a condition which ensures the existence of a positive solutionup concentrating outside the origin atk symmetric points asp goes to +∞. The same techniques lead also to a more general result on general domains. In particular, we find that concentration at the origin is always possible, provided α⊄IN.

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Copyright information

© Hebrew University 2006

Authors and Affiliations

  • Pierpaolo Esposito
    • 1
    • 2
  • Angela Pistoia
    • 3
  • Juncheng Wei
    • 4
  1. 1.Dipartimento di MatematicaUniversità degli Studi “Roma Tre”RomaItaly
  2. 2.Pacific Institute for the Mathematical SciencesUniversity of British ColumbiaVancouverCanada
  3. 3.Dipartimento di Metodi e Modelli MatematiciUniversità di Roma “La Sapienza”RomaItaly
  4. 4.Department of MathematicsChinese University of Hong KongShatin, N.T.Hong Kong

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