On the semilinear Schrödinger equation with time dependent coefficients

Takuya Gonda, Shuji Machihara, Tohru Ozawa

    研究成果: Article

    抄録

    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

    元の言語English
    ページ(範囲)1986-2001
    ページ数16
    ジャーナルMathematische Nachrichten
    287
    発行部数17-18
    DOI
    出版物ステータスPublished - 2014 12 1

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    Semilinear Equations
    Lorentz Spaces
    Integrability
    Coefficient
    Strichartz Estimates
    Contraction Mapping
    Homogeneous Function
    Lebesgue Space
    Existence and Uniqueness of Solutions
    Nonlinear Equations
    Space-time
    Nonlinearity

    ASJC Scopus subject areas

    • Mathematics(all)

    これを引用

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

    :: Mathematische Nachrichten, 巻 287, 番号 17-18, 01.12.2014, p. 1986-2001.

    研究成果: Article

    Gonda, Takuya ; Machihara, Shuji ; Ozawa, Tohru. / On the semilinear Schrödinger equation with time dependent coefficients. :: Mathematische Nachrichten. 2014 ; 巻 287, 番号 17-18. pp. 1986-2001.
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