Nonlinear scalar field equations in ℝN

Mountain pass and symmetric mountain pass approaches

Jun Hirata, Norihisa Ikoma, Kazunaga Tanaka

Research output: Contribution to journalArticle

48 Citations (Scopus)

Abstract

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
Volume35
Issue number2
Publication statusPublished - 2010 Sep 10
Externally publishedYes

Fingerprint

Pohozaev Identity
Mountain Pass
Radially Symmetric Solutions
Scalar Field
Existence Results

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Nonlinear scalar field equations in ℝN : Mountain pass and symmetric mountain pass approaches. / Hirata, Jun; Ikoma, Norihisa; Tanaka, Kazunaga.

In: Topological Methods in Nonlinear Analysis, Vol. 35, No. 2, 10.09.2010, p. 253-276.

Research output: Contribution to journalArticle

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