### 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 |
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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 1 |

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Jeanjean, L., & Tanaka, K. (2003). A remark on least energy solutions in R

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