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Ground State of N Coupled Nonlinear Schrödinger Equations in Rn,n≤3

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An Erratum to this article was published on 07 November 2007

Abstract

We establish some general theorems for the existence and nonexistence of ground state solutions of steady-state N coupled nonlinear Schrödinger equations. The sign of coupling constants β ij ’s is crucial for the existence of ground state solutions. When all β ij ’s are positive and the matrix Σ is positively definite, there exists a ground state solution which is radially symmetric. However, if all β ij ’s are negative, or one of β ij ’s is negative and the matrix Σ is positively definite, there is no ground state solution. Furthermore, we find a bound state solution which is non-radially symmetric when N=3.

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Authors and Affiliations

  1. Department of Mathematics, National Taiwan University, Taipei, Taiwan, R.O.C

    Tai-Chia Lin

  2. Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, P.R. China

    Juncheng Wei

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  1. Tai-Chia Lin
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  2. Juncheng Wei
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Correspondence to Tai-Chia Lin.

Additional information

Communicated by P. Constantin

An erratum to this article is available at http://dx.doi.org/10.1007/s00220-007-0365-5.

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Lin, TC., Wei, J. Ground State of N Coupled Nonlinear Schrödinger Equations in Rn,n≤3. Commun. Math. Phys. 255, 629–653 (2005). https://doi.org/10.1007/s00220-005-1313-x

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