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

Simone Secchi·Marco Squassina
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Abstract

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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Simone Secchi, Marco Squassina. 2004-08-31. On the location of spikes for the Schrodinger equation with electromagnetic field. https://arxiv.org/abs/math/0402253

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