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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.

MSC:

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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