Nonlinear Schrödinger equations and sharp interpolation estimates View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1983-12

AUTHORS

Michael I. Weinstein

ABSTRACT

A sharp sufficient condition for global existence is obtained for the nonlinear Schrödinger equation in the case σ=2/N. This condition is in terms of an exact stationary solution (nonlinear ground state) of (NLS). It is derived by solving a variational problem to obtain the “best constant” for classical interpolation estimates of Nirenberg and Gagliardo. More... »

PAGES

567-576

References to SciGraph publications

  • 1982-12. Orbital stability of standing waves for some nonlinear Schrödinger equations in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1980. Existence of Stationary States in Nonlinear Scalar Field Equations in BIFURCATION PHENOMENA IN MATHEMATICAL PHYSICS AND RELATED TOPICS
  • 1980-12. An estimate for the best constant in a Sobolev inequality involving three integral norms in ANNALI DI MATEMATICA PURA ED APPLICATA (1923 -)
  • 1960-12. An integral formula for total gradient variation in ARCHIV DER MATHEMATIK
  • 1977-06. Existence of solitary waves in higher dimensions in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1972-01. Uniqueness of the ground state solution for Δu−u+u3=0 and a variational characterization of other solutions in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf01208265

    DOI

    http://dx.doi.org/10.1007/bf01208265

    DIMENSIONS

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