A generalised Nehari manifold method for a class of non-linear Schrödinger systems in ℝ3

Tommaso Cortopassi*, Vladimir Georgiev

*この研究の対応する著者

研究成果: Conference contribution

抄録

We study the existence of positive solutions of a particular elliptic system in ℝ3 composed of two non linear stationary Schrödinger equations (NLSEs), that is -∈2Δu + V(x)u = hv(u, v), -∈2Δv + V(x)v = hu(u, v). Under certain hypotheses on the potential V and the non linearity h, we manage to prove that there exists a solution (u∈, v∈) that decays exponentially with respect to local minima points of the potential and whose energy tends to concentrate around these points, as ∈ → 0. We also estimate this energy in terms of particular ground state energies. This work follows closely what is done in [6], although here we consider a more general non linearity and we restrict ourselves to the case where the domain is ℝ3.

本文言語English
ホスト出版物のタイトル8th International Conference New Trends in the Applications of Differential Equations in Sciences, NTADES 2021
編集者Angela Slavova
出版社American Institute of Physics Inc.
ISBN(電子版)9780735441866
DOI
出版ステータスPublished - 2022 4月 5
イベント8th International Conference New Trends in the Applications of Differential Equations in Sciences, NTADES 2021 - St. Constantin and Helena, Bulgaria
継続期間: 2021 9月 62021 9月 10

出版物シリーズ

名前AIP Conference Proceedings
2459
ISSN(印刷版)0094-243X
ISSN(電子版)1551-7616

Conference

Conference8th International Conference New Trends in the Applications of Differential Equations in Sciences, NTADES 2021
国/地域Bulgaria
CitySt. Constantin and Helena
Period21/9/621/9/10

ASJC Scopus subject areas

  • 物理学および天文学一般

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