Cingolani, Silvia; Secchi, Simone; Squassina, Marco Semi-classical limit for Schrödinger equations with magnetic field and Hartree-type nonlinearities. (English) Zbl 1215.35146 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) Cited in 86 Documents 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 PDF BibTeX XML Cite \textit{S. Cingolani} et al., Proc. R. Soc. Edinb., Sect. A, Math. 140, No. 5, 973--1009 (2010; Zbl 1215.35146) Full Text: DOI arXiv OpenURL