On the location of spikes for the Schrodinger equation with electromagnetic field

Details On the location of spikes for the Schrodinger equation with electromagnetic field On the location of spikes for the Schrodinger equation with electromagnetic field

2004-02-16

arxiv.org/abs/math/0402253v3

Mathematics

Analysis of PDEs

Final revision, accepted for publication

Scientific paper

We consider the standing wave solutions of the three dimensional semilinear Schrodinger equation with competing potential functions $V$ and $K$ and under the action of an external electromagnetic vector field $A$. We establish some necessary conditions for a sequence of such solutions to concentrate, in two different senses, around a given point. In the particular but important case of nonlinearities of power type, we prove that the spikes locate at the critical points of a smooth ground energy map independent of $A$.

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