A remark on least energy solutions in RN

Louis Jeanjean; Kazunaga Tanaka

doi:10.1090/S0002-9939-02-06821-1

A remark on least energy solutions in R^N

Louis Jeanjean^*, Kazunaga Tanaka

^*Corresponding author for this work

School of Fundamental Science and Engineering

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

263 Citations (Scopus)

Abstract

We study a mountain pass characterization of least energy solutions of the following nonlinear scalar field equation in R^N -δu = g(u), u ∈ H¹(R^N), where N ≥ 2. Without the assumption of the monotonicity of t → g(t)/t, we show that the mountain pass value gives the least energy level.

Original language	English
Pages (from-to)	2399-2408
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	131
Issue number	8
DOIs	https://doi.org/10.1090/S0002-9939-02-06821-1
Publication status	Published - 2003 Aug

Keywords

Least energy solutions
Mountain pass theorem
Nonlinear elliptic equations in R

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Access to Document

10.1090/S0002-9939-02-06821-1

Cite this

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title = "A remark on least energy solutions in RN",

abstract = "We study a mountain pass characterization of least energy solutions of the following nonlinear scalar field equation in RN -δu = g(u), u ∈ H1(RN), where N ≥ 2. Without the assumption of the monotonicity of t → g(t)/t, we show that the mountain pass value gives the least energy level.",

keywords = "Least energy solutions, Mountain pass theorem, Nonlinear elliptic equations in R",

author = "Louis Jeanjean and Kazunaga Tanaka",

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AU - Tanaka, Kazunaga

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AB - We study a mountain pass characterization of least energy solutions of the following nonlinear scalar field equation in RN -δu = g(u), u ∈ H1(RN), where N ≥ 2. Without the assumption of the monotonicity of t → g(t)/t, we show that the mountain pass value gives the least energy level.

KW - Least energy solutions

KW - Mountain pass theorem

KW - Nonlinear elliptic equations in R

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