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

Cingolani, Silvia; Secchi, Simone; Squassina, Marco

Proc. R. Soc. Edinb., Sect. A, Math. 140, No. 5, 973-1009 (2010).

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.

Reviewer: Marcelo M. Cavalcanti (Maringá)

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

Keywords:

standing wave solutions; Schrödinger equations