### Abstract

We consider nonlinear Schrödinger equation with time dependent coefficients. Fanelli [5] found a transformation between solutions of the original equation and of the usual Schrödinger equation with power nonlinearity involving time dependent coefficients in some Lorentz spaces. In this paper we extend the results in [5] in space-time integrability properties of solutions. Particularly, we prove that the existence and uniqueness of solutions can be described exclusively in terms of Lebesgue spaces (not Lorentz spaces as in [5]) as far as the space integrability of solutions. We also discuss the equation with coefficient of an explicit homogeneous function and describe the associated Strichartz estimate and contraction mapping argument. Copyright

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

Pages (from-to) | 1986-2001 |

Number of pages | 16 |

Journal | Mathematische Nachrichten |

Volume | 287 |

Issue number | 17-18 |

DOIs | |

Publication status | Published - 2014 Dec 1 |

### Fingerprint

### Keywords

- Lorentz space
- Nonlinear Schrödinger equation
- Time dependent coefficient

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Mathematische Nachrichten*,

*287*(17-18), 1986-2001. https://doi.org/10.1002/mana.201200108

**On the semilinear Schrödinger equation with time dependent coefficients.** / Gonda, Takuya; Machihara, Shuji; Ozawa, Tohru.

Research output: Contribution to journal › Article

*Mathematische Nachrichten*, vol. 287, no. 17-18, pp. 1986-2001. https://doi.org/10.1002/mana.201200108

}

TY - JOUR

T1 - On the semilinear Schrödinger equation with time dependent coefficients

AU - Gonda, Takuya

AU - Machihara, Shuji

AU - Ozawa, Tohru

PY - 2014/12/1

Y1 - 2014/12/1

N2 - We consider nonlinear Schrödinger equation with time dependent coefficients. Fanelli [5] found a transformation between solutions of the original equation and of the usual Schrödinger equation with power nonlinearity involving time dependent coefficients in some Lorentz spaces. In this paper we extend the results in [5] in space-time integrability properties of solutions. Particularly, we prove that the existence and uniqueness of solutions can be described exclusively in terms of Lebesgue spaces (not Lorentz spaces as in [5]) as far as the space integrability of solutions. We also discuss the equation with coefficient of an explicit homogeneous function and describe the associated Strichartz estimate and contraction mapping argument. Copyright

AB - We consider nonlinear Schrödinger equation with time dependent coefficients. Fanelli [5] found a transformation between solutions of the original equation and of the usual Schrödinger equation with power nonlinearity involving time dependent coefficients in some Lorentz spaces. In this paper we extend the results in [5] in space-time integrability properties of solutions. Particularly, we prove that the existence and uniqueness of solutions can be described exclusively in terms of Lebesgue spaces (not Lorentz spaces as in [5]) as far as the space integrability of solutions. We also discuss the equation with coefficient of an explicit homogeneous function and describe the associated Strichartz estimate and contraction mapping argument. Copyright

KW - Lorentz space

KW - Nonlinear Schrödinger equation

KW - Time dependent coefficient

UR - http://www.scopus.com/inward/record.url?scp=84913582680&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84913582680&partnerID=8YFLogxK

U2 - 10.1002/mana.201200108

DO - 10.1002/mana.201200108

M3 - Article

AN - SCOPUS:84913582680

VL - 287

SP - 1986

EP - 2001

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

SN - 0025-584X

IS - 17-18

ER -