On the semilinear Schrödinger equation with time dependent coefficients

Takuya Gonda, Shuji Machihara, Tohru Ozawa

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)1986-2001
Number of pages16
JournalMathematische Nachrichten
Volume287
Issue number17-18
DOIs
Publication statusPublished - 2014 Dec 1

Keywords

  • Lorentz space
  • Nonlinear Schrödinger equation
  • Time dependent coefficient

ASJC Scopus subject areas

  • Mathematics(all)

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