Normalized solutions for a system of coupled cubic Schrödinger equations on R3

By Thomas Bartsch, Louis Jeanjean, Nicola Soave. 2016

252 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/813e875c852474fcc5c7901d7a04cc5341f79493

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Normalized solutions for the Chern–Simons–Schrödinger equation in R^2 (2017, background): “In [3], the following coupled cubic Schrödinger systems was considered: { −∆u − λ1u = μ1u(3) + βuv(2), −∆v − λ2v = μ1v(3) + βu(2)v, in R(3).”
Normalized solutions for a Schrödinger equation with critical growth in RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{documen (2021, unknown): “For the reader interested in normalized solutions for the Schrödinger equations, we would also like to refer [9,11,12,17,25,29,31,34,38,39,41] and references therein.”
A natural constraint approach to normalized solutions of nonlinear Schr\"odinger equations and systems (2016, methodology): “In [9] we used in a decisive way the assumption β > 0, and hence we have to modify our argument in the following way.”
Multiple positive normalized solutions for nonlinear Schrödinger systems (2017, background): “Actually under (H0) a second positive solution will be obtained by a mountain-pass argument while under (H1) a linking type procedure, inspired by [5], will be used.”
A global branch approach to normalized solutions for the Schrödinger equation (2021, background): “The results of [7] signiﬁcantly extended the ones of Bartsch et al.[4], which rely on a variational approach on the L 2 -spheres.”
Existence and asymptotic behavior of normalized ground states for Sobolev critical Schrödinger systems (2022, methodology): “We refer the reader to [7, 26, 27, 28, 29, 30, 39, 40, 43] for scalar equations, [8, 9, 10, 11, 14, 21, 22, 31] for systems of two equations, [35] for systems of k equations.”
Normalized solutions to mass supercritical Schrödinger equations with negative potential (2021, background): “After [22], only recently more general autonomous equations and systems have been considered, also refining and developing this initial strategy, see [4, 6, 8, 5, 17, 9, 21, 34, 35] and references therein.”