### 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 ∈ H^{1}(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 | |

Publication status | Published - 2003 Aug |

### Fingerprint

### Keywords

- Least energy solutions
- Mountain pass theorem
- Nonlinear elliptic equations in R

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

^{N}

*Proceedings of the American Mathematical Society*,

*131*(8), 2399-2408. https://doi.org/10.1090/S0002-9939-02-06821-1

**A remark on least energy solutions in R ^{N}
.** / Jeanjean, Louis; Tanaka, Kazunaga.

Research output: Contribution to journal › Article

^{N}',

*Proceedings of the American Mathematical Society*, vol. 131, no. 8, pp. 2399-2408. https://doi.org/10.1090/S0002-9939-02-06821-1

^{N}Proceedings of the American Mathematical Society. 2003 Aug;131(8):2399-2408. https://doi.org/10.1090/S0002-9939-02-06821-1

}

TY - JOUR

T1 - A remark on least energy solutions in RN

AU - Jeanjean, Louis

AU - Tanaka, Kazunaga

PY - 2003/8

Y1 - 2003/8

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=0041743811&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041743811&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-02-06821-1

DO - 10.1090/S0002-9939-02-06821-1

M3 - Article

VL - 131

SP - 2399

EP - 2408

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 8

ER -