Abstract

We will consider the relation between the number of positive standing waves solutions for a class of coupled nonlinear Schrödinger system in RN and the topology of the set of minimum points of potential V (x). The main characteristics of the system are that its functional is strongly indefinite at zero and there is a lack of compactness in RN. Combining the dual variational method with the Nehari technique and using the Concentration-Compactness Lemma, we obtain the existence of multiple solutions associated to the set of global minimum points of the potential V (x) for ε{lunate} sufficiently small. In addition, our result gives a partial answer to a problem raised by Sirakov about existence of solutions of the perturbed system. © 2007 Elsevier Inc. All rights reserved.