Dispersive estimates for Schrödinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three. II
From MaRDI portal
Publication:2479615
DOI10.1007/BF02789446zbMath1146.35324arXivmath/0504585MaRDI QIDQ2479615
Wilhelm Schlag, Mehmet Burak Erdogan
Publication date: 1 April 2008
Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0504585
One-parameter semigroups and linear evolution equations (47D06) A priori estimates in context of PDEs (35B45) PDEs in connection with quantum mechanics (35Q40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)
Related Items (34)
On absence of threshold resonances for Schrödinger and Dirac operators ⋮ Resolvent estimates in amalgam spaces and asymptotic expansions for Schrödinger equations ⋮ Decay estimates for bi-Schrödinger operators in dimension one ⋮ Dispersive Estimates for Four Dimensional Schrödinger and Wave Equations with Obstructions at Zero Energy ⋮ New expressions for the wave operators of Schrödinger operators in \(\mathbb R^3\) ⋮ Dispersive estimates for matrix and scalar Schrödinger operators in dimension five ⋮ Zero resonances for localised potentials ⋮ A critical center-stable manifold for Schrödinger's equation in three dimensions ⋮ A system of ODEs for a perturbation of a minimal mass soliton ⋮ Decay estimates for fourth-order Schrödinger operators in dimension two ⋮ Dispersive estimates for the Schrödinger equation with finite rank perturbations ⋮ On stability of pseudo-conformal blowup for \(L^{2}\)-critical Hartree NLS ⋮ Global dynamics above the ground state energy for the cubic NLS equation in 3D ⋮ Dispersive estimates and asymptotic expansions for Schrödinger equations in dimension one ⋮ Dispersive estimates for massive Dirac operators in dimension two ⋮ New estimates for a time-dependent Schrödinger equation ⋮ Weighted dispersive estimates for two-dimensional Schrödinger operators with Aharonov-Bohm magnetic field ⋮ A centre-stable manifold for the focussing cubic NLS in \({\mathbb{R}}^{1+3\star}\) ⋮ Decay Estimates for the Supercritical 3-D Schrödinger Equation with Rapidly Decreasing Potential ⋮ Strichartz estimates for charge transfer models ⋮ A Dispersive Bound for Three-Dimensional Schrödinger Operators with Zero Energy Eigenvalues ⋮ On eigenfunction expansion of solutions to the Hamilton equations ⋮ Dispersive estimates for inhomogeneous fourth-order Schrödinger operator in 3D with zero energy obstructions ⋮ Decay estimates for higher-order elliptic operators ⋮ Compactons and their variational properties for degenerate KdV and NLS in dimension 1 ⋮ Eigenvalue accumulation and bounds for non-selfadjoint matrix differential operators related to NLS ⋮ On pointwise decay of waves ⋮ Endpoint Strichartz estimates for charge transfer Hamiltonians ⋮ Dispersive estimates for Schrödinger operators in dimension two with obstructions at zero energy ⋮ On the standing waves for nonlinear Hartree equation with confining potential ⋮ Embedded eigenvalues and the nonlinear Schrödinger equation ⋮ Dispersive estimates for higher dimensional Schrödinger operators with threshold eigenvalues. I: The odd dimensional case ⋮ Dispersive estimates for scalar and matrix Schrödinger operators on \(\mathbb H^{n+1}\) ⋮ Pointwise dispersive estimates for Schrödinger operators on product cones
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Dispersive estimates for Schrödinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three. I
- Nonlinear scalar field equations. II: Existence of infinitely many solutions
- Nonlinear scalar field equations. I: Existence of a ground state
- Stable standing waves of nonlinear Klein-Gordon equations
- Dispersive estimates for Schrödinger operators in dimensions one and three
- Stability theory of solitary waves in the presence of symmetry. II
- Orbital stability of standing waves for some nonlinear Schrödinger equations
- Instability of nonlinear bound states
- Stability theory of solitary waves in the presence of symmetry. I
- Uniqueness of positive radial solutions of \(\Delta u+f(u)=0\) in \({\mathbb{R}}^ n\)
- Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
- Spectral properties of Schrödinger operators and time-decay of the wave functions
- Asymptotic expansions in time for solutions of Schrödinger-type equations
- Multichannel nonlinear scattering for nonintegrable equations. II: The case of anisotropic potentials and data
- Existence of solitary waves in higher dimensions
- Local decay of scattering solutions to Schrödinger's equation
- The nonlinear Schrödinger equation. Self-focusing and wave collapse
- Time decay for solutions of Schrödinger equations with rough and time-dependent potentials
- Uniqueness of the ground state solution for \(\Delta u - u + u^3=0\) and a variational characterization of other solutions
- Dispersive estimates for Schrödinger equations with threshold resonance and eigenvalue
- Multichannel nonlinear scattering for nonintegrable equations
- Spectra of positive and negative energies in the linearized NLS problem
- Asymptotic Stability of Multi-soliton Solutions for Nonlinear Schrödinger Equations
- Bifurcations from the endpoints of the essential spectrum in the linearized nonlinear Schrödinger problem
- Modulational Stability of Ground States of Nonlinear Schrödinger Equations
- Lyapunov stability of ground states of nonlinear dispersive evolution equations
- Linearized instability for nonlinear schrödinger and klein-gordon equations
- Decay estimates for Schrödinger operators
- A UNIFIED APPROACH TO RESOLVENT EXPANSIONS AT THRESHOLDS
- Purely nonlinear instability of standing waves with minimal energy
- A spectral mapping theorem and invariant manifolds for nonlinear Schrodinger equations
- Dispersive analysis of charge transfer models
- Stabilization of solutions to nonlinear Schrödinger equations
- The \(W^{k,p}\)-continuity of wave operators for Schrödinger operators
- On the formation of singularities in solutions of the critical nonlinear Schrödinger equation
This page was built for publication: Dispersive estimates for Schrödinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three. II