Optimal number of solutions for nonlinear coupled Schrödinger systems. I: Synchronized case
type: Item
instance of: scholarly article
title: Optimal number of solutions for nonlinear coupled Schrödinger systems. I: Synchronized case
zbMATH Open document ID: 1421.35069
author: Zhongwei Tang
author: Lushun Wang
published in: Journal of Differential Equations
publication date: 2019-01-22T00:00:00Z
review text: This paper is concerned with the study of a class of semilinear Schrödinger systems with Neumann boundary condition. The main result of this paper establishes a sufficient condition for the existence of positive solutions in the cooperative case. A key tool in the arguments is played by the Lyapunov-Schmidt reduction method.
reviewed by: Vicenţiu D. Rădulescu
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 35J57
Mathematics Subject Classification ID: 35J20
zbMATH DE Number: 7005210
zbMATH Keywords: semilinear Schrödinger systems
zbMATH Keywords: Neumann condition
zbMATH Keywords: Lyapunov-Schmidt reduction
zbMATH Keywords: synchronized solution
MaRDI profile type: Publication
full work available at URL: j.jde.2018.09.018
OpenAlex ID: W2894299907
cites work: Stability of periodic optical solitons for a nonlinear Schrödinger system
cites work: An optimal bound on the number of interior spike solutions for the Lin-Ni-Takagi problem
cites work: Semi-classical standing waves for nonlinear Schrödinger systems
cites work: Q3630719
cites work: A Liouville theorem, a-priori bounds, and bifurcating branches of positive solutions for a nonlinear elliptic system
cites work: On a min-max procedure for the existence of a positive solution for certain scalar field equations in \({\mathbb{R}}^ N\)
cites work: Bound states for a coupled Schrödinger system
cites work: Ground states of nonlinear Schrödinger systems
cites work: Blowup and solitary wave solutions with ring profiles of two-component nonlinear Schrödinger systems
cites work: Infinitely many sign-changing and semi-nodal solutions for a nonlinear Schrödinger system
cites work: High frequency solutions for the singularly-perturbed one-dimensional nonlinear Schrödinger equation
cites work: On the number of positive solutions of singularly perturbed 1D NLS
cites work: Existence and orbital stability of standing waves for nonlinear Schrödinger systems
cites work: Q3923023
cites work: Q4040640
cites work: Multiple interior peak solutions for some singularly perturbed Neumann problems.
cites work: Existence and uniqueness of positive solutions of nonlinear Schrödinger systems
cites work: On the number of interior peak solutions for a singularly perturbed Neumann problem
cites work: Spikes in two coupled nonlinear Schrödinger equations
cites work: Multiple bound states of nonlinear Schrödinger systems
cites work: Minimal energy solutions for repulsive nonlinear Schrödinger systems
cites work: From the Klein-Gordon-Zakharov system to a singular nonlinear Schrödinger system
cites work: On the shape of least‐energy solutions to a semilinear Neumann problem
cites work: Locating the peaks of least-energy solutions to a semilinear Neumann problem
cites work: Orbital stability of solitary waves for a nonlinear Schrödinger system
cites work: Segregated and synchronized vector solutions for nonlinear Schrödinger systems
cites work: Least energy solitary waves for a system of nonlinear Schrödinger equations in \({\mathbb{R}^n}\)
cites work: Least Energy Solutions for Nonlinear Schrödinger Systems with Mixed Attractive and Repulsive Couplings
cites work: Spike-layer solutions to singularly perturbed semilinear systems of coupled Schrödinger equations
cites work: Multi-peak solutions to coupled Schrödinger systems with Neumann boundary conditions
cites work: Segregated peak solutions of coupled Schrödinger systems with Neumann boundary conditions
cites work: Number of synchronized and segregated interior spike solutions for nonlinear coupled elliptic systems
cites work: Uniqueness of positive solutions to some coupled nonlinear Schrödinger equations
DOI: 10.1016/J.JDE.2018.09.018
description: scientific article; zbMATH DE number 7005210