### Abstract

For m > 0 and p ∈ (1, (N + 2)/(N - 2)), we show the uniqueness and a linearized non-degeneracy of solutions for the following problem: δu - |x|^{m}u + u^{p} = 0, u > 0 in ℝ^{N} and lim |x|→∞ u(x) = 0.

Original language | English |
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Pages (from-to) | 975-987 |

Number of pages | 13 |

Journal | Proceedings of the Royal Society of Edinburgh Section A: Mathematics |

Volume | 138 |

Issue number | 5 |

DOIs | |

Publication status | Published - Oct 2008 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Uniqueness of standing waves for nonlinear Schrdinger equations.** / Byeon, Jaeyoung; Oshita, Yoshihito.

Research output: Contribution to journal › Article

*Proceedings of the Royal Society of Edinburgh Section A: Mathematics*, vol. 138, no. 5, pp. 975-987. https://doi.org/10.1017/S0308210507000236

}

TY - JOUR

T1 - Uniqueness of standing waves for nonlinear Schrdinger equations

AU - Byeon, Jaeyoung

AU - Oshita, Yoshihito

PY - 2008/10

Y1 - 2008/10

N2 - For m > 0 and p ∈ (1, (N + 2)/(N - 2)), we show the uniqueness and a linearized non-degeneracy of solutions for the following problem: δu - |x|mu + up = 0, u > 0 in ℝN and lim |x|→∞ u(x) = 0.

AB - For m > 0 and p ∈ (1, (N + 2)/(N - 2)), we show the uniqueness and a linearized non-degeneracy of solutions for the following problem: δu - |x|mu + up = 0, u > 0 in ℝN and lim |x|→∞ u(x) = 0.

UR - http://www.scopus.com/inward/record.url?scp=53849097034&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=53849097034&partnerID=8YFLogxK

U2 - 10.1017/S0308210507000236

DO - 10.1017/S0308210507000236

M3 - Article

VL - 138

SP - 975

EP - 987

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

SN - 0308-2105

IS - 5

ER -