Semi-classical limit for Schrödinger equations with magnetic field and Hartree-type nonlinearities. (English) Zbl 1215.35146

The authors study the semi-classical regime of standing wave solutions of a Schrödinger equation in the presence of non-constant electric and magnetic potentials, 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.


35Q55 NLS equations (nonlinear Schrödinger equations)
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
35B35 Stability in context of PDEs
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