### Abstract

We construct a local theory of the Cauchy problem for the nonlinear Schrödinger equations with α ∈ (1, 5) and u _{0} ∈ L{frown} ^{p}(ℝ) when p lies in an open neighborhood of 2. Moreover we prove the global existence for the initial value problem when p is sufficiently close to 2.

Original language | English |
---|---|

Pages (from-to) | 3905-3920 |

Number of pages | 16 |

Journal | Proceedings of the American Mathematical Society |

Volume | 140 |

Issue number | 11 |

DOIs | |

Publication status | Published - 2012 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

^{p}-initial data.

*Proceedings of the American Mathematical Society*,

*140*(11), 3905-3920. https://doi.org/10.1090/S0002-9939-2012-11314-0

**On existence of global solutions of schrödinger equations with subcritical nonlinearity for L{frown} ^{p}-initial data.** / Hyakuna, Ryosuke; Tsutsumi, Masayoshi.

Research output: Contribution to journal › Article

^{p}-initial data',

*Proceedings of the American Mathematical Society*, vol. 140, no. 11, pp. 3905-3920. https://doi.org/10.1090/S0002-9939-2012-11314-0

}

TY - JOUR

T1 - On existence of global solutions of schrödinger equations with subcritical nonlinearity for L{frown} p-initial data

AU - Hyakuna, Ryosuke

AU - Tsutsumi, Masayoshi

PY - 2012

Y1 - 2012

N2 - We construct a local theory of the Cauchy problem for the nonlinear Schrödinger equations with α ∈ (1, 5) and u 0 ∈ L{frown} p(ℝ) when p lies in an open neighborhood of 2. Moreover we prove the global existence for the initial value problem when p is sufficiently close to 2.

AB - We construct a local theory of the Cauchy problem for the nonlinear Schrödinger equations with α ∈ (1, 5) and u 0 ∈ L{frown} p(ℝ) when p lies in an open neighborhood of 2. Moreover we prove the global existence for the initial value problem when p is sufficiently close to 2.

UR - http://www.scopus.com/inward/record.url?scp=84863936063&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84863936063&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-2012-11314-0

DO - 10.1090/S0002-9939-2012-11314-0

M3 - Article

VL - 140

SP - 3905

EP - 3920

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 11

ER -