Skip to main content
SpringerLink
Log in

Classical solutions of nonlinear Schrödinger equations

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

We prove the existence of global classical solutions to the initial value problem for the nonlinear Schrödinger equation, iut−Δu+q(|u|2)u=0 in iut - Δu + (|u|2)u = in (t, x)ɛℝxℝn for 6≦n≦11.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bergh, J. and Löfström, J.: Interpolation Spaces. Berlin, Heidelberg, New York: Springer 1976

    Google Scholar 

  2. Brenner, P. and Wahl, W. von: Global classical solutions of nonlinear wave equations. Math. Z. 176, 87–121 (1981)

    Google Scholar 

  3. Friedman, A.: Partial Differential Equations: Holt, Rinehart and Winston, New York, 1969

    Google Scholar 

  4. Ginibre, J. and Velo, G.: On the class of nonlinear Schrödinger equations I, II. J. Functional Analysis 32, 1–32, 33–71 (1979)

    Google Scholar 

  5. Lin, J.E. and Strauss, W.A.: Decay and scattering of solutions of a nonlinear Schrödinger equation. J. Functional Analysis 30, 245–263(1978)

    Google Scholar 

  6. Mizohata, S.: Theory of Partial Differential Equations: Iwanami (1965) (in Japanese)

  7. Pecher, H. and Wahl, W. von: Time dependent nonlinear Schrödinger equations. Manuscripta Math. 27, 125–157 (1979)

    Google Scholar 

  8. Segal, I.E.: Nonlinear semi-groups. Ann. Math. 78, 339–364(1963)

    Google Scholar 

  9. Strauss, W.A.: The nonlinear Schrödinger equation. In Proceedings of the International Symposium on Continuum Mechanics and Partial Differential Equations (Rio de Janeiro 1977), 452–465. Amsterdam, New York, Oxford: North Holland 1978

    Google Scholar 

  10. Tsutsumi, M. and Hayashi, N.: Classical solutions of nonlinear Schrödinger equations in higher dimensions. Math. Z. 177, 217–234(1981)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Physics, Waseda University, 160, Tokyo, Japan

    Nakao Hayashi

Authors
  1. Nakao Hayashi
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hayashi, N. Classical solutions of nonlinear Schrödinger equations. Manuscripta Math 55, 171–190 (1986). https://doi.org/10.1007/BF01168683

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01168683

Keywords

Search

Navigation