Multiple complex-valued solutions for nonlinear magnetic Schrödinger equations

Silvia Cingolani, Louis Jeanjean, Kazunaga Tanaka*

*この研究の対応する著者

研究成果: Article査読

7 被引用数 (Scopus)

抄録

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 C1 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 ⊂ RN 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.

本文言語English
ページ(範囲)37-66
ページ数30
ジャーナルJournal of Fixed Point Theory and Applications
19
1
DOI
出版ステータスPublished - 2017 3月 1

ASJC Scopus subject areas

  • モデリングとシミュレーション
  • 幾何学とトポロジー
  • 応用数学

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