Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

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

Silvia Cingolania1, Simone Secchia2 and Marco Squassinaa3

a1 Dipartimento di Matematica, Politecnico di Bari, Via Orabona 4, 70125 Bari, Italy (s.cingolani@poliba.it)

a2 Dipartimento di Matematica ed Applicazioni, Università di Milano Bicocca, Via R. Cozzi 53 edificio U5, 20125 Milan, Italy (simone.secchi@unimib.it)

a3 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.

(Received March 31 2009)

(Accepted November 09 2009)