Multiple solutions and their limiting behavior of coupled nonlinear Schrödinger systems

We study the multiplicity of positive solutions and their limiting behavior as ɛ tends to zero for a class of coupled nonlinear Schrödinger system in RN. We relate the number of positive solutions to the topology of the set of minimum points of the least energy function for ɛ sufficiently small. Also, we verify that these solutions concentrate at a global minimum point of the least energy function.