A note on a mountain pass characterization of least energy solutions

Louis Jeanjean; Kazunaga Tanaka

doi:10.1515/ans-2003-0403

A note on a mountain pass characterization of least energy solutions

Louis Jeanjean^*, Kazunaga Tanaka

^*Corresponding author for this work

School of Fundamental Science and Engineering

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

32 Citations (Scopus)

Abstract

We consider the equation -u" = g(u), u(x) ∈ H¹(R). (0.1) Under general assumptions on the nonlinearity g we prove that the, unique up to translation, solution of (0.1) is at the mountain pass level of the associated functional. This result extends a corresponding result for least energy solutions when (0.1) is set on R^N.

Original language	English
Pages (from-to)	445-455
Number of pages	11
Journal	Advanced Nonlinear Studies
Volume	3
Issue number	4
DOIs	https://doi.org/10.1515/ans-2003-0403
Publication status	Published - 2003

Keywords

Least energy solution
Mountain pass characterization

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematics(all)

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10.1515/ans-2003-0403

Cite this

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AB - We consider the equation -u" = g(u), u(x) ∈ H1(R). (0.1) Under general assumptions on the nonlinearity g we prove that the, unique up to translation, solution of (0.1) is at the mountain pass level of the associated functional. This result extends a corresponding result for least energy solutions when (0.1) is set on RN.

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A note on a mountain pass characterization of least energy solutions

Abstract

Keywords

ASJC Scopus subject areas

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