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

Jun Hirata; Norihisa Ikoma; Kazunaga Tanaka

Nonlinear scalar field equations in ℝ^N: Mountain pass and symmetric mountain pass approaches

Jun Hirata, Norihisa Ikoma, Kazunaga Tanaka

Research output: Contribution to journal › Article › peer-review

Abstract

We study the existence of radially symmetric solutions of the following nonlinear scalar field equations in ℝ^N : -Δu = g(u) in ℝ^N', u ∈ H¹ (ℝ^N). 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 language	English
Pages (from-to)	253-276
Number of pages	24
Journal	Topological Methods in Nonlinear Analysis
Volume	35
Issue number	2
Publication status	Published - 2010 Sept 10
Externally published	Yes

Keywords

Minimax methods
Nonlinear scalar field equations
Radially symmetric solutions

ASJC Scopus subject areas

Analysis
Applied Mathematics

Cite this

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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. GaIlo{\"u}e'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.",

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author = "Jun Hirata and Norihisa Ikoma and Kazunaga Tanaka",

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AU - Hirata, Jun

AU - Ikoma, Norihisa

AU - Tanaka, Kazunaga

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Y1 - 2010/9/10

N2 - 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.

AB - 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.

KW - Minimax methods

KW - Nonlinear scalar field equations

KW - Radially symmetric solutions

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ER -

Nonlinear scalar field equations in ℝ^N: Mountain pass and symmetric mountain pass approaches

Abstract

Keywords

ASJC Scopus subject areas

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