Bubbling solutions for an elliptic equation with exponential Neumann data in R^2

• Shengbing Deng ^[1] ; Monica Musso ^[2]
  1. [1] Universidad de Chile

     Universidad de Chile

     Santiago, Chile

     
  2. [2] Pontificia Universidad Católica de Chile

     Pontificia Universidad Católica de Chile

     Santiago, Chile

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 13, Nº 3, 2014, págs. 699-744
• Idioma: inglés
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• Resumen

  • Let  be a bounded domain in R2 with smooth boundary; we study the following Neumann problem 8>< >:

    −1u + u = 0 in  @u @⌫ = %u p−1eu p on @, (0.1) where ⌫ is the outer normal vector of @, % > 0 is a small parameter and 0 < p < 2. We construct bubbling solutions to problem (0.1) by a Lyapunov-Schmidt reduction procedure.