### Abstract

We study, in the semiclassical limit, the singularly perturbed nonlinear Schrödinger equations (Formula presented.)where (Formula presented.), (Formula presented.) is the Schrödinger operator with a magnetic field having source in a (Formula presented.) vector potential A and a scalar continuous (electric) potential V defined by (Formula presented.)Here, f is a nonlinear term which satisfies the so-called Berestycki-Lions conditions. We assume that there exists a bounded domain (Formula presented.) such that (Formula presented.)and we set (Formula presented.). For (Formula presented.) small we prove the existence of at least (Formula presented.) geometrically distinct, complex-valued solutions to (0.1) whose moduli concentrate around K as (Formula presented.).

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

Pages (from-to) | 1-30 |

Number of pages | 30 |

Journal | Journal of Fixed Point Theory and Applications |

DOIs | |

Publication status | Accepted/In press - 2016 Nov 14 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Modelling and Simulation
- Geometry and Topology
- Applied Mathematics

### Cite this

*Journal of Fixed Point Theory and Applications*, 1-30. https://doi.org/10.1007/s11784-016-0347-3

**Multiple complex-valued solutions for nonlinear magnetic Schrödinger equations.** / Cingolani, Silvia; Jeanjean, Louis; Tanaka, Kazunaga.

Research output: Contribution to journal › Article

*Journal of Fixed Point Theory and Applications*, pp. 1-30. https://doi.org/10.1007/s11784-016-0347-3

}

TY - JOUR

T1 - Multiple complex-valued solutions for nonlinear magnetic Schrödinger equations

AU - Cingolani, Silvia

AU - Jeanjean, Louis

AU - Tanaka, Kazunaga

PY - 2016/11/14

Y1 - 2016/11/14

N2 - We study, in the semiclassical limit, the singularly perturbed nonlinear Schrödinger equations (Formula presented.)where (Formula presented.), (Formula presented.) is the Schrödinger operator with a magnetic field having source in a (Formula presented.) vector potential A and a scalar continuous (electric) potential V defined by (Formula presented.)Here, f is a nonlinear term which satisfies the so-called Berestycki-Lions conditions. We assume that there exists a bounded domain (Formula presented.) such that (Formula presented.)and we set (Formula presented.). For (Formula presented.) small we prove the existence of at least (Formula presented.) geometrically distinct, complex-valued solutions to (0.1) whose moduli concentrate around K as (Formula presented.).

AB - We study, in the semiclassical limit, the singularly perturbed nonlinear Schrödinger equations (Formula presented.)where (Formula presented.), (Formula presented.) is the Schrödinger operator with a magnetic field having source in a (Formula presented.) vector potential A and a scalar continuous (electric) potential V defined by (Formula presented.)Here, f is a nonlinear term which satisfies the so-called Berestycki-Lions conditions. We assume that there exists a bounded domain (Formula presented.) such that (Formula presented.)and we set (Formula presented.). For (Formula presented.) small we prove the existence of at least (Formula presented.) geometrically distinct, complex-valued solutions to (0.1) whose moduli concentrate around K as (Formula presented.).

KW - Complex-valued solutions

KW - Cuplength

KW - Magnetic fields

KW - Nonlinear Schrödinger equations

KW - Semiclassical limit

UR - http://www.scopus.com/inward/record.url?scp=84995414745&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84995414745&partnerID=8YFLogxK

U2 - 10.1007/s11784-016-0347-3

DO - 10.1007/s11784-016-0347-3

M3 - Article

SP - 1

EP - 30

JO - Journal of Fixed Point Theory and Applications

JF - Journal of Fixed Point Theory and Applications

SN - 1661-7738

ER -