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

Pietro d'Avenia·Alessio Pomponio·David Ruiz
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Abstract

In this paper we study semiclassical states for the problem $$ -\eps^2 Δu + V(x) u = f(u) \qquad \hbox{in} \RN,$$ 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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Pietro d'Avenia, Alessio Pomponio, David Ruiz. 2012-03-09. Semi-classical states for the Nonlinear Schrödinger Equation on saddle points of the potential via variational methods. https://arxiv.org/abs/1107.5652

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