A complete classification of ground-states for a coupled nonlinear Schrödinger system
A complete classification of ground-states for a coupled nonlinear Schrödinger system
In this paper, we establish the existence of nontrivial ground-state solutions for a coupled nonlinear Schrödinger system$-\Delta u_j+ u_j=\sum\limits_{i=1}^mb_{ij}u_i^2u_j, \quad\text{in}\ \mathbb{R}^n,\\ u_j(x)\to 0\ \text{as}\ |x|\ \to \infty, \quad j=1,2,\cdots, m,$where $n=1, 2, 3, m\geq 2$ and $b_{ij}$ are positive constants satisfying $b_{ij}=b_{ji}.$ By nontrivial we mean a solution that has …