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

研究成果: Article › 査読

抄録

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.

本文言語	English
ページ（範囲）	253-276
ページ数	24
ジャーナル	Topological Methods in Nonlinear Analysis
巻	35
号	2
出版ステータス	Published - 2010 9月 10
外部発表	はい

ASJC Scopus subject areas

分析
応用数学

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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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language = "English",

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T2 - Mountain pass and symmetric mountain pass approaches

AU - Hirata, Jun

AU - Ikoma, Norihisa

AU - Tanaka, Kazunaga

PY - 2010/9/10

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

UR - https://www.scopus.com/pages/publications/77956325764

UR - https://www.scopus.com/pages/publications/77956325764#tab=citedBy

M3 - Article

AN - SCOPUS:77956325764

SN - 1230-3429

VL - 35

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EP - 276

JO - Topological Methods in Nonlinear Analysis

JF - Topological Methods in Nonlinear Analysis

IS - 2

ER -

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

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