Multiplicity of positive solutions of nonlinear Schrodinger equations concentrating at a potential well

We consider singularly perturbed nonlinear Schrodinger equations where and is a nonlinear term which satisfies the so-called Berestycki-Lions conditions. We assume that there exists a bounded domain such that and we set . For small we prove the existence of at least solutions to (0.1) concentrating, as around . We remark that, under our assumptions of , the search of solutions to (0.1) cannot be reduced to the study of the critical points of a functional restricted to a Nehari manifold.