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

Manuel del Pino, Monica Musso, Carlos Román, Juncheng Wei

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1 Citation (SciVal)

Abstract

We consider the problem of finding positive solutions of the problem Δu − λu + u 5 = 0 in a bounded, smooth domain Ω in ℝ 3 , 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 λ − λ * > 0 is sufficiently small, then this problem is solvable by a solution u λ which blows-up by bubbling at a certain interior point of Ω as λ ↓ λ * .

Original languageEnglish
Pages (from-to)813-843
Number of pages31
JournalJournal d'Analyse Mathematique
Volume137
Issue number2
DOIs
Publication statusPublished - 1 Mar 2019

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)

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