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In this paper we study semiclassical states for the problem $$ -\eps^2 \Deltau + V(x) u = f(u) \qquad \hbox{in} \RN,$$ where $f(u)$ is a superlinearnonlinear term. Under our hypotheses on $f$ a Lyapunov-Schmidt reduction is notpossible. We use variational methods to prove the existence of spikes aroundsaddle points of the potential $V(x)$.

Semi-classical states for the Nonlinear Schr\"odinger Equation on saddle points of the potential via variational methods