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Journal d'Analyse Mathématique

, Volume 137, Issue 2, pp 813–843 | Cite as

Interior bubbling solutions for the critical Lin-Ni-Takagi problem in dimension 3

  • Manuel del Pino
  • Monica MussoEmail author
  • Carlos Román
  • Juncheng Wei
Article
  • 16 Downloads

Abstract

We consider the problem of finding positive solutions of the problem Δuλu + u5 = 0 in a bounded, smooth domain Ω in ℝ3, under zero Neumann boundary conditions. Here λ is a positive number. We analyze the role of Green’s function of −Δ + λ in the presence of solutions exhibiting single bubbling behavior at one point of the domain when λ is regarded as a parameter. As a special case of our results, we find and characterize a positive value λ* such that if λλ* > 0 is sufficiently small, then this problem is solvable by a solution uλ which blows-up by bubbling at a certain interior point of Ω as λλ*.

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Copyright information

© The Hebrew University of Jerusalem 2019

Authors and Affiliations

  • Manuel del Pino
    • 1
  • Monica Musso
    • 2
    Email author
  • Carlos Román
    • 3
  • Juncheng Wei
    • 4
  1. 1.Departamento deIngeniería Matemática, and Centro de Modelamiento Matemático (UMI 2807 CNRS)Universidad de ChileSantiagoChile
  2. 2.Departmento de MatemáticasPontificia Universidad Católica de ChileSantiagoChile
  3. 3.Sorbonne Universités UPMC Univ Paris 06 CNRS, UMR 7598, Laboratoire Jacques-Louis LionsParisFrance
  4. 4.Department of MathematicsUniversity of British ColumbiaVancouverCanada

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