The semi-classical regime of standing wave solutions of a Schr¨odinger 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.
Cingolani, S., Secchi, S., Squassina, M., Semiclassical limit for Schrodinger equations with a magnetic field and Hartree-type nonlinearities, <<PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS>>, 2010; 140 (5): 973-1009. [doi:10.1017/S0308210509000584] [http://hdl.handle.net/10807/89960]
Semiclassical limit for Schrodinger equations with a magnetic field and Hartree-type nonlinearities
Squassina, MarcoUltimo
2010
Abstract
The semi-classical regime of standing wave solutions of a Schr¨odinger 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.
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