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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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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DOI: https://doi.org/10.1007/s00220-005-1313-x