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 field B. 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, the spikes locate at the critical points of a smooth ground energy map independent of B.

Secchi, S., Squassina, M., On the location of spikes for the Schrodinger equation with electromagnetic field, <<COMMUNICATIONS IN CONTEMPORARY MATHEMATICS>>, 2005; 7 (N/A): 251-268 [http://hdl.handle.net/10807/91014]

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

S.; Squassina
Ultimo
2005

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 field B. 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, the spikes locate at the critical points of a smooth ground energy map independent of B.
Inglese
Secchi, S., Squassina, M., On the location of spikes for the Schrodinger equation with electromagnetic field, <<COMMUNICATIONS IN CONTEMPORARY MATHEMATICS>>, 2005; 7 (N/A): 251-268 [http://hdl.handle.net/10807/91014]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/91014
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