Ground States and Bound States of a Nonlinear Schrödinger System

Abstract This paper concerns existence and multiplicity of ground states and bound states of the time-independent Schrödinger system where n = 2, 3, N ≥ 2, λj > 0 for j = 1, ... , N, βjj > 0 for j = 1, ... , N, and βij = βji. 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.