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Time dependent nonlinear Schrödinger equations

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Abstract

We prove the existence of global classical solutions of the Cauchy-problem for nonlinear Schrödinger equations u′+iAu+f(|u|2)u or u′+Au+if(|u|2)u respectively. We need various growth conditions on the nonlinearity f and some restrictions on the admissible space dimension n.

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References

  1. BROWDER, F.E.: On the spectral theory of elliptic differential operators I. Math. Ann.142, 22–130 (1961)

    Google Scholar 

  2. FRIEDMAN, A.: Partial differential equations. Holt, Rinehart and Winston, New York (1969)

    Google Scholar 

  3. LIONS, J.L.: Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, Gauthier-Villars, Paris (1969)

    Google Scholar 

  4. PECHER, H.: Globale klassische Lösungen nichtlinearer Wellengleichungen für höhere Raumdimensionen. Nachr. Akad. Wiss. Göttingen, II. Math.-Phys. Klasse Nr.14, 221–232 (1975)

    Google Scholar 

  5. PECHER, H.: LP-Abschätzungen und klassische Lösungen für nichtlineare Wellengleichungen I. Math. Z.150, 159–183 (1976)

    Google Scholar 

  6. von WAHL, W.: Über nichtlineare Wellengleichungen mit zeitabhängigem elliptischen Hauptteil. Math. Z.142, 105–120 (1975)

    Google Scholar 

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Authors and Affiliations

  1. Fachbereich Mathematik der Gesamthochschule, Gaußstraße 20, D-5600, Wuppertal 1, Fed. Rep. of Germany

    Hartmut Pecher

  2. Fachbereich Mathematik und Physik der Universität, Postfach 3008, D-8580, Bayreuth, Fed. Rep. of Germany

    Wolf von Wahl

Authors
  1. Hartmut Pecher
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  2. Wolf von Wahl
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Pecher, H., von Wahl, W. Time dependent nonlinear Schrödinger equations. Manuscripta Math 27, 125–157 (1979). https://doi.org/10.1007/BF01299292

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  • DOI: https://doi.org/10.1007/BF01299292

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