(untitled) (Analysis in Theory and Applications, 2021)
In this paper, we study the following N-coupled nonlinear Schrödinger system where n≤3, N≥3, μ_j>0, β_i, j=β_j, i>0 are constants and β_j, j=μ_j, j=1, …, N. There have been intensive studies for the system on existence/non-existence and classification of ground state solutions when N=2. However, fewer results about the classification of ground state solution are available for N≥3. In this paper, we first give a complete classification result on ground state solutions with Morse indices 1, 2 or 3 for three-coupled Schrödinger system. Then we generalize our results to N-coupled Schrödinger system for ground state solutions with Morse indices 1 and N. We show that any positive ground state solutions with Morse index 1 or Morse index N must be the form of (d_1w,d_2w,…,d_Nw) under suitable conditions, where w is the unique positive ground state solution of certain equation. Finally, we generalize our results to fractional N-coupled Schrödinger system.