Semi-classical states for the Nonlinear Schrödinger Equation on saddle points of the potential via variational methods

Details Semi-classical states for the Nonlinear Schrödinger Equation on saddle points of the potential via variational methods Semi-classical states for the Nonlinear Schrödinger Equation on saddle points of the potential via variational methods

2011-07-28

arxiv.org/abs/1107.5652v2

Mathematics

Analysis of PDEs

pre-peer version, to appear in J. Funct. Anal

Scientific paper

In this paper we study semiclassical states for the problem $$ -\eps^2 \Delta
u + V(x) u = f(u) \qquad \hbox{in} \RN,$$ 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 $V(x)$.

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