Semi-classical standing waves for nonlinear Schrödinger equations at structurally stable critical points of the potential.

We consider a singularly perturbed elliptic equation Berestycki-Lions [3] found almost necessary and sufficient conditions on the nonlinearity f for existence of a solution of the limiting problem. There have been endeavors to construct solutions of the singularly perturbed problem concentrating around structurally stable critical points of the potential V under possibly general conditions on f. In this paper, we prove that under the optimal conditions of Berestycki-Lions on f 2 C1, there exists a solution concentrating around topologically stable positive critical points of V, whose critical values are characterized by minimax methods. [ABSTRACT FROM AUTHOR]