Nonstandard solutions for a perturbed nonlinear Schrödinger system with small coupling coefficients

DOI10.1002/mana.202000121arXiv1807.05644MaRDI QIDQ6057917

Chunhua Wang, Xiaoming An

Publication date: 5 October 2023

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.05644

zbMATH Keywords

variational methodsSchrödinger systemspenalized techniqueconcentrating synchronouslysmall coupling coefficients

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Singular perturbations in context of PDEs (35B25) Variational methods for elliptic systems (35J50) Second-order elliptic equations (35J15) Semilinear elliptic equations (35J61)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• New existence and symmetry results for least energy positive solutions of Schrödinger systems with mixed competition and cooperation terms
• Bifurcation in a multicomponent system of nonlinear Schrödinger equations
• Semi-classical states for the Choquard equation
• Nonlinear Schrödinger equation: concentration on circles driven by an external magnetic field
• Multi-peak bound states for Schrödinger equations with compactly supported or unbounded potentials
• Nonlinear scalar field equations. I: Existence of a ground state
• Perturbation methods and semilinear elliptic problems on \(\mathbb R^n\)
• Semiclassical stationary states for nonlinear Schrödinger equations with fast decaying potentials
• Positive solutions for a weakly coupled nonlinear Schrödinger system
• Bound states for a coupled Schrödinger system
• Groundstates for the nonlinear Schrödinger equation with potential vanishing at infinity
• Radial solutions and phase separation in a system of two coupled Schrödinger equations
• Existence of solitary waves in higher dimensions
• Semi-classical states for nonlinear Schrödinger equations
• Semiclassical states of nonlinear Schrödinger equations
• Construction of solutions via local Pohozaev identities
• Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential
• Local mountain passes for semilinear elliptic problems in unbounded domains
• Minimax theorems
• Segregated and synchronized vector solutions for nonlinear Schrödinger systems
• Minimal energy solutions for cooperative nonlinear Schrödinger systems
• Multiple normalized solutions for quasi-linear Schrödinger equations
• Least energy solitary waves for a system of nonlinear Schrödinger equations in \({\mathbb{R}^n}\)
• Semiclassical states for weakly coupled nonlinear Schrödinger systems
• Bound states of nonlinear Schrödinger equations with potentials vanishing at infinity
• Spherical semiclassical states of a critical frequency for Schrödinger equations with decaying potentials
• Uniqueness of the ground state solution for \(\Delta u - u + u^3=0\) and a variational characterization of other solutions
• Ground state of \(N\) coupled nonlinear Schrödinger equations in \(\mathbb R^n\), \(n \leq 3\)
• Ground States and Bound States of a Nonlinear Schrödinger System
• Semi-Classical Bound States for Schrödinger Equations with Potentials Vanishing or Unbounded at Infinity
• Homoclinic Orbits for Second Order Hamiltonian Systems Possessing Superquadratic Potentials
• On Concentration of Positive Bound States of Nonlinear Schrödinger Equations with Competing Potential Functions
• Least Energy Solutions for Nonlinear Schrödinger Systems with Mixed Attractive and Repulsive Couplings
• Standing waves of some coupled nonlinear Schrödinger equations
• Local uniqueness and periodicity induced by concentration
• Multiplicity results for some nonlinear Schrödinger equations with potentials

This page was built for publication: Nonstandard solutions for a perturbed nonlinear Schrödinger system with small coupling coefficients