Multiple normalized solutions for a Sobolev critical Schrödinger equation
From MaRDI portal
Publication:2171005
DOI10.1007/s00208-021-02228-0zbMath1497.35433arXiv2011.02945OpenAlexW3174234974MaRDI QIDQ2171005
Louis Jeanjean, Thanh Trung Le
Publication date: 8 September 2022
Published in: Mathematische Annalen (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2011.02945
Stability in context of PDEs (35B35) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38) Blow-up in context of PDEs (35B44) Time-dependent Schrödinger equations and Dirac equations (35Q41)
Related Items (34)
On Existence of Multiple Normalized Solutions to a Class of Elliptic Problems in Whole \(\mathbb{R}^N\) via Lusternik-Schnirelmann Category ⋮ The existence and asymptotic behaviours of normalized solutions for critical fractional Schrödinger equation with Choquard term ⋮ Normalized ground state for the Sobolev critical Schrödinger equation involving Hardy term with combined nonlinearities ⋮ Mass threshold of the limit behavior of normalized solutions to Schrödinger equations with combined nonlinearities ⋮ Prescribed mass solutions to Schrödinger systems with linear coupled terms ⋮ Multiple normalized solutions for biharmonic Choquard equation with Hardy-Littlewood-Sobolev upper critical and combined nonlinearities ⋮ Normalized ground states for a Hardy-Littlewood-Sobolev upper critical Schrödinger equation with double Choquard type nonlinear terms ⋮ Normalized solutions for a critical fractional Choquard equation with a nonlocal perturbation ⋮ Prescribed mass standing waves for energy critical Hartree equations ⋮ Normalized ground state solutions for critical growth Schrödinger equations ⋮ Normalized solutions for Schrödinger equations with mixed dispersion and critical exponential growth in \(\mathbb{R}^2\) ⋮ Normalized ground states for Sobolev critical nonlinear Schrödinger equation in the \(L^2\)-supercritical case ⋮ Normalized solutions for Kirchhoff type equations with combined nonlinearities: the Sobolev critical case ⋮ Standing waves with prescribed norm for the coupled Hartree-Fock system ⋮ Multiplicity and stability of normalized solutions to non-autonomous Schrödinger equation with mixed non-linearities ⋮ Multiple normalized solutions for the planar Schrödinger-Poisson system with critical exponential growth ⋮ Normalized ground states and multiple solutions for nonautonomous fractional Schrödinger equations ⋮ Normalized Solutions for Schrödinger Equations with Critical Exponential Growth in \(\boldsymbol{\mathbb{R}^2}\) ⋮ Normalized solutions of nonhomogeneous mass supercritical Schrödinger equations in bounded domains ⋮ Normalized solutions to fractional Schrödinger equation with potentials ⋮ On the Kirchhoff equation with prescribed mass and general nonlinearities ⋮ Normalized solutions for nonlinear Schrödinger equation involving potential and Sobolev critical exponent ⋮ Normalized solutions to planar Schrödinger equation with exponential critical nonlinearity ⋮ Normalized ground states for the mass-energy doubly critical Kirchhoff equations ⋮ Normalized solutions to the Chern-Simons-Schrödinger system under the nonlinear combined effect ⋮ Standing waves with prescribed \(L^2\)-norm to nonlinear Schrödinger equations with combined inhomogeneous nonlinearities ⋮ Normalized solutions for critical growth Schrödinger equations with nonautonomous perturbation ⋮ Asymptotic profiles for a nonlinear Kirchhoff equation with combined powers nonlinearity ⋮ Another look at Schrödinger equations with prescribed mass ⋮ Multiple normalized solutions for the coupled Hartree-Fock system with upper critical exponent ⋮ Normalized solutions for \((p,q)\)-Laplacian equations with mass supercritical growth ⋮ A global branch approach to normalized solutions for the Schrödinger equation ⋮ Existence and asymptotic behavior of normalized ground states for Sobolev critical Schrödinger systems ⋮ Existence, stability and asymptotic behaviour of normalized solutions for the Davey-Stewartson system
Cites Work
- Normalized solutions for a system of coupled cubic Schrödinger equations on \(\mathbb R^3\)
- Solitons and scattering for the cubic-quintic nonlinear Schrödinger equation on \({\mathbb{R}^3}\)
- Existence of a ground state solution for a nonlinear scalar field equation with critical growth
- Nonlinear scalar field equations. II: Existence of infinitely many solutions
- Nonlinear scalar field equations. I: Existence of a ground state
- The concentration-compactness principle in the calculus of variations. The locally compact case. I
- The concentration-compactness principle in the calculus of variations. The locally compact case. II
- Orbital stability of standing waves for some nonlinear Schrödinger equations
- On nonhomogeneous elliptic equations involving critical Sobolev exponent
- Multiple normalized solutions for a competing system of Schrödinger equations
- Existence of a ground state and scattering for a nonlinear Schrödinger equation with critical growth
- Orbital stability of ground states for a Sobolev critical Schrödinger equation
- Normalized ground states for the NLS equation with combined nonlinearities: the Sobolev critical case
- Normalized ground states for the NLS equation with combined nonlinearities
- Solitary waves and dynamics for subcritical perturbations of energy critical NLS
- The double-power nonlinear Schrödinger equation and its generalizations: uniqueness, non-degeneracy and applications
- On the normalized ground states of second order PDE's with mixed power non-linearities
- On Dipolar Quantum Gases in the Unstable Regime
- Existence and instability of standing waves with prescribed norm for a class of Schrödinger-Poisson equations
- Symmetric decreasing rearrangement can be discontinuous
- A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
- Existence of solutions with prescribed norm for semilinear elliptic equations
- Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
- A Note on Berestycki-Cazenave's Classical Instability Result for Nonlinear Schrödinger Equations
- Symmetric Decreasing Rearrangement Is Sometimes Continuous
- Normalized solutions for nonlinear Schrödinger systems on bounded domains
- On the Variational Approach to the Stability of Standing Waves for the Nonlinear Schrödinger Equation
- Global dynamics above the ground state energy for the combined power-type nonlinear Schrödinger equations with energy-critical growth at low frequencies
- Stationary Waves with Prescribed $L^2$-Norm for the Planar Schrödinger--Poisson System
- Strong instability of standing waves with negative energy for double power nonlinear Schr\"odinger equations
- Nonradial normalized solutions for nonlinear scalar field equations
- The Nonlinear Schrödinger Equation with Combined Power-Type Nonlinearities
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Multiple normalized solutions for a Sobolev critical Schrödinger equation
