Multiple complex-valued solutions for nonlinear magnetic Schrödinger equations

Silvia Cingolani; Louis Jeanjean; Kazunaga Tanaka

doi:10.1007/s11784-016-0347-3

Multiple complex-valued solutions for nonlinear magnetic Schrödinger equations

Silvia Cingolani, Louis Jeanjean, Kazunaga Tanaka

Research output: Contribution to journal › Article

2 Citations (Scopus)

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	https://doi.org/10.1007/s11784-016-0347-3
Publication status	Accepted/In press - 2016 Nov 14

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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

Cingolani, S., Jeanjean, L., & Tanaka, K. (Accepted/In press). Multiple complex-valued solutions for nonlinear magnetic Schrödinger equations. Journal of Fixed Point Theory and Applications, 1-30. https://doi.org/10.1007/s11784-016-0347-3

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AU - Tanaka, Kazunaga

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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.).

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10.1007/s11784-016-0347-3