Nonlinear scalar field equations in ℝN: Mountain pass and symmetric mountain pass approaches

Jun Hirata, Norihisa Ikoma, Kazunaga Tanaka

Research output: Contribution to journalArticlepeer-review

74 Citations (Scopus)


We study the existence of radially symmetric solutions of the following nonlinear scalar field equations in ℝN : -Δu = g(u) in ℝN', u ∈ H1 (ℝN). We give an extension of the existence results due to H. Berestycki, T. GaIloüe't and O. Kavian [2]. We take a mountain pass approach in H1(ℝ N) and introduce a new method generating a Palais-Smale sequence with an additional property related to Pohozaev identity.

Original languageEnglish
Pages (from-to)253-276
Number of pages24
JournalTopological Methods in Nonlinear Analysis
Issue number2
Publication statusPublished - 2010 Sep 10
Externally publishedYes


  • Minimax methods
  • Nonlinear scalar field equations
  • Radially symmetric solutions

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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