Semiclassical states for the nonlinear Schr?dinger equation on saddle points of the potential via variational methods

摘要

In this paper we study semiclassical states for the problem where f(u) is a superlinear nonlinear term. Under our hypotheses on f a Lyapunov-Schmidt reduction is not possible. We use variational methods to prove the existence of spikes around saddle points of the potential V(x).