### Abstract

We study, in the semiclassical limit, the singularly perturbed nonlinear Schrödinger equations LA,Vħu=f(|u|2)uinRNwhere N≥ 3 , LA,Vħ is the Schrödinger operator with a magnetic field having source in a C^{1} vector potential A and a scalar continuous (electric) potential V defined by LA,Vħ=-ħ2Δ-2ħiA·∇+|A|2-ħidivA+V(x).Here, f is a nonlinear term which satisfies the so-called Berestycki-Lions conditions. We assume that there exists a bounded domain Ω ⊂ R^{N} such that (Formula presented.). For ħ> 0 small we prove the existence of at least cupl (K) + 1 geometrically distinct, complex-valued solutions to (0.1) whose moduli concentrate around K as ħ→ 0.

Original language | English |
---|---|

Pages (from-to) | 37-66 |

Number of pages | 30 |

Journal | Journal of Fixed Point Theory and Applications |

Volume | 19 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2017 Mar 1 |

### Keywords

- Complex-valued solutions
- Cuplength
- Magnetic fields
- Nonlinear Schrödinger equations
- Semiclassical limit

### ASJC Scopus subject areas

- Modelling and Simulation
- Geometry and Topology
- Applied Mathematics

## Fingerprint Dive into the research topics of 'Multiple complex-valued solutions for nonlinear magnetic Schrödinger equations'. Together they form a unique fingerprint.

## Cite this

*Journal of Fixed Point Theory and Applications*,

*19*(1), 37-66. https://doi.org/10.1007/s11784-016-0347-3