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

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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 $A$.
Final revision, accepted for publication

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Analysis of PDEs, 35J65, 35Q40, 35Q55, 83C50

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http://salesiana.dossiersoluciones.com/handle/123456789/70183

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0402253
 http://arxiv.org/abs/math/0402253

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arXiv