Semilinear Schrödinger equations with a potential of some critical inverse-square type

DOI10.1016/j.jde.2019.11.087zbMath1435.35358OpenAlexW2991192260MaRDI QIDQ2306685

Toshiyuki Suzuki

Publication date: 24 March 2020

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2019.11.087

zbMATH Keywords

semilinear Schrödinger equationsenergy methodsStrichartz estimatesHartree equationsinverse-square potentialsradial-spherical decomposition

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Perturbation theories for operators and differential equations in quantum theory (81Q15)

Related Items (5)

Semilinear Schrödinger equations with a critical scale of the singular electromagnetic field ⋮ The Cauchy problem for Choquard equation with an inverse‐square potential ⋮ Qualitative analysis of solutions to a nonlocal Choquard–Kirchhoff diffusion equations in ℝN$$ {\mathbb{R}}^N $$ ⋮ Semilinear Schrödinger evolution equations with inverse-square and harmonic potentials via pseudo-conformal symmetry ⋮ Initial-boundary value problem for a fourth-order plate equation with Hardy-Hénon potential and polynomial nonlinearity

Cites Work

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• Scattering theory for nonlinear Schrödinger equations with inverse-square potential
• Orbital stability for the Schrödinger operator involving inverse square potential
• The energy-critical NLS with inverse-square potential
• Uniform resolvent estimates for magnetic Schrödinger operators and smoothing effects for related evolution equations
• Minimal mass blow-up solutions for the \(L^2\) critical NLS with inverse-square potential
• Weighted Strichartz estimates for the Schrödinger and wave equations on Damek-Ricci spaces
• Sharp constants in the Hardy-Rellich inequalities
• Best constants in some operator smoothness estimates
• Three integrable Hamiltonian systems connected with isospectral deformations
• Strichartz estimates for the wave and Schrödinger equations with the inverse-square potential
• Scattering in \(H^{1}\) for the intercritical NLS with an inverse-square potential
• Sobolev spaces adapted to the Schrödinger operator with inverse-square potential
• Energy methods for abstract nonlinear Schrödinger equations
• Remarks on endpoint Strichartz estimates for Schrödinger equations with the critical inverse-square potential
• Kato smoothing and Strichartz estimates for wave equations with magnetic potentials
• The energy-critical nonlinear wave equation with an inverse-square potential
• The focusing cubic NLS with inverse-square potential in three space dimensions.
• Energy methods for Hartree type equations with inverse-square potentials
• Global existence and blowup for a class of the focusing nonlinear Schrödinger equation with inverse-square potential
• Wave operators and similarity for some non-selfadjoint operators
• Convolution operators and L(p, q) spaces
• Notes on some inequalities for linear operators
• Solvability of Nonlinear Schrödinger Equations with Some Critical Singular Potential via Generalized Hardy-Rellich Inequalities
• Some Hardy inequalities on the sphere
• Cauchy problem for nonlinear Schrödinger equations with inverse-square potentials
• Endpoint Strichartz estimates
• Spherically Averaged Endpoint Strichartz Estimates For The TwoDimensional Schrödinger Equation
• On stability and instability of standing waves for the nonlinear Schrödinger equation with an inverse-square potential
• Focusing NLS with inverse square potential
• Virial identities for nonlinear Schrödinger equations with a critical coefficient inverse-square potential
• The nonlinear Schrödinger equation with an inverse-square potential
• Erratum: Solution of the one-dimensional N-body problems with quadratic and/or inversely quadratic pair potentials [J. Math. Phys. 12, 419–436 (1971)]
• Blowup of nonlinear Schrödinger equations with inverse-square potentials
• Strichartz estimates for the wave and Schroedinger equations with potentials of critical decay
• Maximal functions associated to filtrations
• Horizon states for AdS black holes
• Near-horizon conformal structure of black holes
• The fundamental solution and Strichartz estimates for the Schrödinger equation on flat Euclidean cones

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