Existence of standing waves for coupled nonlinear Schrödinger equations

DOI10.3836/tjm/1279719580zbMath1198.35257OpenAlexW1966370996MaRDI QIDQ989201

Norihisa Ikoma

Publication date: 30 August 2010

Published in: Tokyo Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3836/tjm/1279719580

zbMATH Keywords

coupled nonlinear Schrödinger equationsstanding wavesleast energy solutionNehari type manifold

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) NLS equations (nonlinear Schrödinger equations) (35Q55) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Positive solutions to PDEs (35B09)

Related Items (5)

Distributional solutions of the stationary nonlinear Schrödinger equation: singularities, regularity and exponential decay ⋮ A local mountain pass type result for a system of nonlinear Schrödinger equations ⋮ Standing waves for weakly coupled nonlinear Schrödinger systems ⋮ Positive solutions for Schrödinger system with asymptotically periodic potentials ⋮ Uniqueness of positive solutions for a nonlinear elliptic system

Cites Work

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• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• Positive solutions for a weakly coupled nonlinear Schrödinger system
• Existence and concentration of ground states of coupled nonlinear Schrödinger equations
• Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
• Critical point theory and Hamiltonian systems
• On a class of nonlinear Schrödinger equations
• On the existence of a positive solution of semilinear elliptic equations in unbounded domains
• Symmetry results for semilinear elliptic systems in the whole space
• Singularly perturbed elliptic problems with superlinear or asymptotically linear nonlinearities
• Minimax theorems
• Bound and ground states of coupled nonlinear Schrödinger equations
• Least energy solitary waves for a system of nonlinear Schrödinger equations in \({\mathbb{R}^n}\)
• Ground state of \(N\) coupled nonlinear Schrödinger equations in \(\mathbb R^n\), \(n \leq 3\)
• Nonconvex minimization problems
• Solitary waves andNcoupled nonlinear equations
• Existence and multiplicity results for some superlinear elliptic problems on R^N
• Standing waves of some coupled nonlinear Schrödinger equations

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