Multi-peak solutions for coupled nonlinear Schrödinger systems in low dimensions

DOI10.1007/s00245-023-09974-4OpenAlexW4362733025MaRDI QIDQ2701077

Maoding Zhen, Vicenţiu D. Rădulescu, Binlin Zhang

Publication date: 27 April 2023

Published in: Applied Mathematics and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00245-023-09974-4

zbMATH Keywords

Lyapunov-Schmidt reductionattractive and repulsive cases

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Singular perturbations in context of PDEs (35B25) Semilinear elliptic equations (35J61) Second-order elliptic systems (35J47)

Cites Work

• On entire solutions of an elliptic system modeling phase separations
• On elliptic systems with Sobolev critical growth
• Nonradial symmetric bound states for a system of coupled Schrödinger equations
• Spikes in two-component systems of nonlinear Schrödinger equations with trapping potentials
• Spike vector solutions for some coupled nonlinear Schrödinger equations
• Bound states for a coupled Schrödinger system
• Infinitely many solutions for the prescribed scalar curvature problem on \(\mathbb S^N\)
• Radial solutions and phase separation in a system of two coupled Schrödinger equations
• Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
• Existence and uniqueness results on single-peaked solutions of a semilinear problem
• Existence, non-degeneracy of proportional positive solutions and least energy solutions for a fractional elliptic system
• Multiple normalized solutions for a competing system of Schrödinger equations
• Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential
• Multiplicity of positive and nodal solutions for nonlinear elliptic problems in \(\mathbb{R}^ N\)
• Segregated and synchronized vector solutions for nonlinear Schrödinger systems
• Uniqueness of positive solutions to some coupled nonlinear Schrödinger equations
• Multi-scale spike solutions for nonlinear coupled elliptic systems with critical frequency
• Normalized solutions for nonlinear coupled fractional systems: low and high perturbations in the attractive case
• Standing waves for semilinear Schrödinger equations with discontinuous dispersion
• First and second critical exponents for an inhomogeneous Schrödinger equation with combined nonlinearities
• Ground states of nonlinear Schrödinger systems with mixed couplings
• A Liouville theorem, a-priori bounds, and bifurcating branches of positive solutions for a nonlinear elliptic system
• Infinitely many positive solutions for the nonlinear Schrödinger equations in \(\mathbb R^N\)
• Nonlinear time-harmonic Maxwell equations in an anisotropic bounded medium
• Entire nonradial solutions for non-cooperative coupled elliptic system with critical exponents in \(\mathbb R^3\)
• Least energy solitary waves for a system of nonlinear Schrödinger equations in \({\mathbb{R}^n}\)
• Spikes in two coupled nonlinear Schrödinger equations
• Ground state of \(N\) coupled nonlinear Schrödinger equations in \(\mathbb R^n\), \(n \leq 3\)
• Solutions with multiple peaks for nonlinear elliptic equations
• On Positive Multipeak Solutions of a Nonlinear Elliptic Problem
• The existence, uniqueness and nonexistence of the ground state to theN-coupled Schrödinger systems in $ \newcommand{\R}{{\mathbb R}} \boldsymbol{\R^n (n\leqslant 4)}$
• Many synchronized vector solutions for a Bose–Einstein system
• On coupled nonlinear Schrödinger systems with mixed couplings
• Entropy solutions for elliptic Schrödinger type equations under Fourier boundary conditions

This page was built for publication: Multi-peak solutions for coupled nonlinear Schrödinger systems in low dimensions