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Global Dynamics Above the Ground State for the Nonlinear Klein–Gordon Equation Without a Radial Assumption

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Abstract

We extend our result Nakanishi and Schlag in J. Differ. Equ. 250(5):2299–2333, 2011) to the non-radial case, giving a complete classification of global dynamics of all solutions with energy that is at most slightly above that of the ground state for the nonlinear Klein–Gordon equation with the focusing cubic nonlinearity in three space dimensions.

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Authors and Affiliations

  1. Department of Mathematics, Kyoto University, Kyoto, 606-8502, Japan

    K. Nakanishi

  2. Department of Mathematics, The University of Chicago, Chicago, IL, 60615, USA

    W. Schlag

Authors
  1. K. Nakanishi
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  2. W. Schlag
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Correspondence to W. Schlag.

Additional information

Communicated by V. Šverák

The second author was supported in part by the National Science Foundation, DMS-0617854 as well as by a Guggenheim fellowship.

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Nakanishi, K., Schlag, W. Global Dynamics Above the Ground State for the Nonlinear Klein–Gordon Equation Without a Radial Assumption. Arch Rational Mech Anal 203, 809–851 (2012). https://doi.org/10.1007/s00205-011-0462-7

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  • DOI: https://doi.org/10.1007/s00205-011-0462-7

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