## 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 |
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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 |

## ASJC Scopus subject areas

- General Mathematics
- Applied Mathematics

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