Bubble tower solutions for supercritical elliptic problem in R^N

• Wenjing Chen ^[1] ; Juan Dávila ^[2] ; Ignacio Guerra ^[3]
  1. [1] Southwest University

     Southwest University

     China

     
  2. [2] Universidad de Chile

     Universidad de Chile

     Santiago, Chile

     
  3. [3] Universidad de Santiago de Chile

     Universidad de Santiago de Chile

     Santiago, Chile

     

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• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 15, Nº Extra 1 (Special volume), 2016, págs. 85-116
• Idioma: inglés
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• Resumen

  • We consider the problem ( −1u + u = u p + "uq u > 0 in RN u(z) !0 as |z| !1 where p = p⇤ + ", with p⇤ = N+2 N−2 , while 1 < q < N+2 N−2 if N % 4, and 3 < q < 5 if N = 3, " > 0, and " is a positive parameter. We prove that for " > 0 small enough, the problem has a solution with the shape of a tower of bubbles.