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

Tommaso Cortopassi*, Vladimir Georgiev

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish
Title of host publication8th International Conference New Trends in the Applications of Differential Equations in Sciences, NTADES 2021
EditorsAngela Slavova
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735441866
DOIs
Publication statusPublished - 2022 Apr 5
Event8th International Conference New Trends in the Applications of Differential Equations in Sciences, NTADES 2021 - St. Constantin and Helena, Bulgaria
Duration: 2021 Sep 62021 Sep 10

Publication series

NameAIP Conference Proceedings
Volume2459
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

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

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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