Normalized solutions to the mixed dispersion nonlinear Schrödinger equation in the mass critical and supercritical regime
From MaRDI portal
Publication:4967319
DOI10.1090/tran/7769zbMath1420.35343arXiv1802.09217OpenAlexW2963017613MaRDI QIDQ4967319
Denis Bonheure, Tian-Xiang Gou, Jean-Baptiste Castéras, Louis Jeanjean
Publication date: 3 July 2019
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1802.09217
PDEs in connection with optics and electromagnetic theory (35Q60) Stability in context of PDEs (35B35) Variational methods for elliptic systems (35J50) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Higher-order elliptic equations (35J30) Positive solutions to PDEs (35B09)
Related Items
Exact Number of Positive Solutions for the Kirchhoff Equation ⋮ Normalized solutions to the Chern-Simons-Schrödinger system ⋮ Non-homogeneous Gagliardo-Nirenberg inequalities in \(\mathbb{R}^N\) and application to a biharmonic non-linear Schrödinger equation ⋮ Normalized solutions for Schrödinger equations with critical Sobolev exponent and mixed nonlinearities ⋮ Normalized solutions for a class of scalar field equations involving mixed fractional Laplacians ⋮ Normalized ground states for the NLS equation with combined nonlinearities: the Sobolev critical case ⋮ Quasilinear Schrödinger equations: ground state and infinitely many normalized solutions ⋮ Mass threshold of the limit behavior of normalized solutions to Schrödinger equations with combined nonlinearities ⋮ Normalized ground states for the NLS equation with combined nonlinearities ⋮ Normalized solutions to biharmonic Schrödinger equation with critical growth in \(\mathbb{R}^N\) ⋮ The existence and stability of normalized solutions for a bi-harmonic nonlinear Schrödinger equation with mixed dispersion ⋮ Normalized solutions to the fractional Schrödinger equations with combined nonlinearities ⋮ Normalized solutions for nonlinear Schrödinger equations on graphs ⋮ Normalized solutions to the nonlinear Choquard equations with Hardy-Littlewood-Sobolev upper critical exponent ⋮ Normalized ground states to the \(p\)-Laplacian equation with general nonlinearities ⋮ Normalized solutions for the mixed dispersion nonlinear Schrödinger equations with four types of potentials and mass subcritical growth ⋮ Normalized solutions for a fourth-order Schrödinger equation with a positive second-order dispersion coefficient ⋮ Existence and dynamics of normalized solutions to nonlinear Schrödinger equations with mixed fractional Laplacians ⋮ Standing waves with prescribed \(L^2\)-norm to nonlinear Schrödinger equations with combined inhomogeneous nonlinearities ⋮ Existence and multiplicity of normalized solutions to biharmonic Schrödinger equations with subcritical growth ⋮ Existence and stability of normalized solutions to the mixed dispersion nonlinear Schrödinger equations ⋮ Existence and stability of standing waves for the mixed dispersion nonlinear Schrödinger equation with a partial confinement in \(\mathbb{R}^N\) ⋮ Existence and instability of normalized standing waves for the fractional Schrödinger equations in the L2-supercritical case ⋮ Strong instability of standing waves for a fourth-order nonlinear Schrödinger equation with the mixed dispersions ⋮ Ground states for a nonlocal mixed order cubic-quartic Gross-Pitaevskii equation ⋮ A mass supercritical problem revisited ⋮ Uncountably many solutions for nonlinear Helmholtz and curl-curl equations ⋮ On a fourth‐order nonlinear Helmholtz equation ⋮ Normalized solutions of supercritical nonlinear fractional Schrödinger equation with potential ⋮ Periodic and asymptotically periodic fourth-order Schrödinger equations with critical and subcritical growth ⋮ Normalized ground states of nonlinear biharmonic Schrödinger equations with Sobolev critical growth and combined nonlinearities ⋮ Existence, stability and asymptotic behaviour of normalized solutions for the Davey-Stewartson system ⋮ On the standing waves for the X-ray free electron laser Schrödinger equation ⋮ A sharp Gagliardo-Nirenberg inequality and its application to fractional problems with inhomogeneous nonlinearity ⋮ Radial and non-radial multiple solutions to a general mixed dispersion NLS equation
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Stable solitary waves with prescribed \(L^2\)-mass for the cubic Schrödinger system with trapping potentials
- Normalized solutions for a system of coupled cubic Schrödinger equations on \(\mathbb R^3\)
- Maximizers for Gagliardo-Nirenberg inequalities and related non-local problems
- A natural constraint approach to normalized solutions of nonlinear Schrödinger equations and systems
- Asymptotic behavior of oscillating radial solutions to certain nonlinear equations. II.
- Oscillating solutions for nonlinear Helmholtz equations
- Nonlinear scalar field equations. II: Existence of infinitely many solutions
- Nonlinear Schrödinger equations and sharp interpolation estimates
- Nonlinear scalar field equations. I: Existence of a ground state
- The concentration-compactness principle in the calculus of variations. The locally compact case. II
- Global well-posedness for energy critical fourth-order Schrödinger equations in the radial case
- Some estimates and maximum principles for weakly coupled systems of elliptic PDE
- Symmetry results for semilinear elliptic systems in the whole space
- Stability of solitons described by nonlinear Schrödinger-type equations with higher-order dispersion
- Normalized bound states for the nonlinear Schrödinger equation in bounded domains
- Unstable normalized standing waves for the space periodic NLS
- Correction to: ``A natural constraint approach to normalized solutions of nonlinear Schrödinger equations and systems
- Normalized solutions of nonlinear Schrödinger equations
- Nonexistence and optimal decay of supersolutions to Choquard equations in exterior domains
- Stabilization of soliton instabilities by higher order dispersion: KdV-type equations.
- Existence and orbital stability of the ground states with prescribed mass for the \(L^2\)-critical and supercritical NLS on bounded domains
- Dual variational methods and nonvanishing for the nonlinear Helmholtz equation
- Sharp nonexistence results of prescribed \(L^2\)-norm solutions for some class of Schrödinger-Poisson and quasi-linear equations
- Spectral and scattering theory for Schrödinger operators
- On Dipolar Quantum Gases in the Unstable Regime
- Existence and instability of standing waves with prescribed norm for a class of Schrödinger-Poisson equations
- Scattering theory for the fourth-order Schrödinger equation in low dimensions
- EXISTENCE OF STEADY STATES FOR THE MAXWELL–SCHRÖDINGER–POISSON SYSTEM: EXPLORING THE APPLICABILITY OF THE CONCENTRATION–COMPACTNESS PRINCIPLE
- Singular solutions of theL2-supercritical biharmonic nonlinear Schrödinger equation
- Ring-type singular solutions of the biharmonic nonlinear Schrödinger equation
- THE MASS-CRITICAL FOURTH-ORDER SCHRÖDINGER EQUATION IN HIGH DIMENSIONS
- Existence of solutions with prescribed norm for semilinear elliptic equations
- Self-Focusing with Fourth-Order Dispersion
- The Fourth-Order Dispersive Nonlinear Schrödinger Equation: Orbital Stability of a Standing Wave
- Stability and instability results for standing waves of quasi-linear Schrödinger equations
- Normalized solutions for nonlinear Schrödinger systems
- Orbitally Stable Standing Waves of a Mixed Dispersion Nonlinear Schrödinger Equation
- Dispersion estimates for fourth order Schrödinger equations
- On a fourth‐order nonlinear Helmholtz equation
- Blowup for Biharmonic NLS
- Ground state and non-ground state solutions of some strongly coupled elliptic systems
- Singular Solutions of the Biharmonic Nonlinear Schrödinger Equation
- Waveguide solutions for a nonlinear Schrödinger equation with mixed dispersion
- Strong Instability of Ground States to a Fourth Order Schrödinger Equation
