We consider a singularly perturbed elliptic equation
where for any The singularly perturbed problem has corresponding limiting problems
Berestycki-Lions found almost necessary and sufficient conditions on nonlinearity 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 potential under possibly general conditions on . In this paper, we prove that under the optimal conditions of Berestycki-Lions on , there exists a solution concentrating around topologically stable positive critical points of , whose critical values are characterized by minimax methods.
Cite this article
Jaeyoung Byeon, Kazunaga Tanaka, Semi-classical standing waves for nonlinear Schrödinger equations at structurally stable critical points of the potential. J. Eur. Math. Soc. 15 (2013), no. 5, pp. 1859–1899DOI 10.4171/JEMS/407