Ground States and Bound States of a Nonlinear Schrödinger System

This paper concerns existence and multiplicity of ground states and bound states of the time-independent Schrödinger system where n = 2, 3, N ≥ 2, λ j > 0 for j = 1, ... , N, β jj > 0 for j = 1, ... , N, and β ij = β ji . In the attractive case we give sufficient condition for existence of co-existing ground states with large couplings, and in the repulsive case we prove existence of infinitely many co-existing bound state solutions with arbitrary couplings.