Ground states and concentration phenomena for the fractional Schrödinger equation

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Date
2014
Journal Title
Journal ISSN
Volume Title
Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract

We consider here solutions of the nonlinear fractional Schrödinger equation. We show that concentration points must be critical points for the potential. We also prove that, if the potential is coercive and has a unique global minimum, then ground states concentrate suitably at such minimal point. In addition, if the potential is radial, then the minimizer is unique.

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Keywords
Fractional Laplacian, ground states, concentration phenomena, uniqueness
Citation
Citation
Fall, M. M., Mahmoudi, F., & Valdinoci, E. (2014). Ground states and concentration phenomena for the fractional Schrödinger equation (Version publishedVersion, Vol. 2031). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
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