Ground State of N Coupled Nonlinear Schrödinger Equations in Rn , n ≤ 3
نویسندگان
چکیده
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 βij ’s is crucial for the existence of ground state solutions. When all βij ’s are positive and the matrix is positively definite, there exists a ground state solution which is radially symmetric. However, if all βij ’s are negative, or one of βij ’s is negative and the matrix 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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