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Semi-classical limit for Schrödinger equations with magnetic field and Hartree-type nonlinearities

Published online by Cambridge University Press:  01 October 2010

Silvia Cingolani
Affiliation:
Dipartimento di Matematica, Politecnico di Bari, Via Orabona 4, 70125 Bari, Italy (s.cingolani@poliba.it)
Simone Secchi
Affiliation:
Dipartimento di Matematica ed Applicazioni, Università di Milano Bicocca, Via R. Cozzi 53 edificio U5, 20125 Milan, Italy (simone.secchi@unimib.it)
Marco Squassina
Affiliation:
Dipartimento di Informatica, Università di Verona, Cà Vignal 2, Strada Le Grazie 15, 37134 Verona, Italy (marco.squassina@univr.it)

Abstract

The semi-classical regime of standing wave solutions of a Schrödinger equation in the presence of non-constant electric and magnetic potentials is studied in the case of non-local nonlinearities of Hartree type. It is shown that there exists a family of solutions having multiple concentration regions which are located around the minimum points of the electric potential.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2010

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