Semiclassical states for the nonlinear Schrödinger equation on saddle points of the potential via variational methods

In this paper we study semiclassical states for the problem −ε2 u +V (x)u = f (u) in N, 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). © 2012 Elsevier Inc. All rights reserved.