Direct methods for pseudo-relativistic Schrödinger operators

DOI10.1007/s12220-020-00492-1zbMath1475.35314arXiv2002.09924OpenAlexW3047784567MaRDI QIDQ2048260

Guolin Qin, Wei Dai, Dan Wu

Publication date: 5 August 2021

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.09924

zbMATH Keywords

epigraphdirect methods of moving planes3D boson star equationsdirect sliding methodspseudo-relativistic Schrödinger operators

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Galactic and stellar structure (85A15) Fractional partial differential equations (35R11) Symmetries, invariants, etc. in context of PDEs (35B06) Ginzburg-Landau equations (35Q56) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53) Bosonic systems in quantum theory (81V73)

Related Items (23)

Liouville-type results for positive solutions of pseudo-relativistic Schrödinger system ⋮ Monotonicity and nonexistence of positive solutions for pseudo-relativistic equation with indefinite nonlinearity ⋮ Symmetry and monotonicity of positive solutions for a class of general pseudo-relativistic systems ⋮ On properties of positive solutions to nonlinear tri-harmonic and bi-harmonic equations with negative exponents ⋮ Radial symmetry of a relativistic Schrödinger tempered fractional p-Laplacian model with logarithmic nonlinearity ⋮ Maximum principles and the method of moving planes for the uniformly elliptic nonlocal Bellman operator and applications ⋮ Monotonicity and symmetry of positive solutions to fractional p-Laplacian equation ⋮ Monotonicity and uniqueness of positive solutions to elliptic fractional \(p\)-equations ⋮ Existence and stability of traveling waves for semi-relativistic Schrödinger equations with van der Waals-type potentials ⋮ Symmetry and monotonicity of positive solutions to systems involving general pseudo-relativistic operators ⋮ Maximum principles and qualitative properties of solutions for nonlocal double phase operator ⋮ Nonexistence of solutions for tempered fractional parabolic equations ⋮ Maximum principles involving the uniformly elliptic nonlocal operator ⋮ Asymptotic symmetry and monotonicity of solutions for weighted fractional parabolic equations ⋮ Monotonicity of solutions for the system with pseudo-relativistic Schrödinger operators ⋮ Asymptotic method of moving planes for fractional parabolic equations ⋮ Nonexistence of solutions for indefinite fractional parabolic equations ⋮ Symmetry and monotonicity of nonnegative solutions to pseudo-relativistic Choquard equations ⋮ Liouville theorem involving the uniformly nonlocal operator ⋮ Sliding methods for a class of generalized fractional Laplacian equations ⋮ Monotonicity of solutions for fractional \(p\)-equations with a gradient term ⋮ Maximum principles and Liouville results for uniformly elliptic nonlocal Bellman system ⋮ Normalized ground states for general pseudo-relativistic Schrödinger equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unique continuation properties for relativistic Schrödinger operators with a singular potential
• Sharp essential self-adjointness of relativistic Schrödinger operators with a singular potential
• Multiplicity results for elliptic fractional equations with subcritical term
• A direct method of moving planes for the fractional Laplacian
• Fractional Laplacian in conformal geometry
• On De Giorgi's conjecture in dimension \(N\geq 9\)
• Relativistic Schrödinger operators: Asymptotic behavior of the eigenfunctions
• Uniqueness of ground states for pseudorelativistic Hartree equations
• Classification of positive solitary solutions of the nonlinear Choquard equation
• Ground state solutions of scalar field fractional Schrödinger equations
• Existence and stability of standing waves for nonlinear fractional Schrödinger equations with Hartree type nonlinearity
• Monotonicity, symmetry and antisymmetry of solutions of semilinear elliptic equations
• Hartree-Fock theory for pseudorelativistic atoms
• Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
• Positive solutions of nonlinear problems involving the square root of the Laplacian
• Well-posedness for semi-relativistic Hartree equations of critical type
• Symmetry and asymmetry: the method of moving spheres
• Liouville-type theorems and harnack-type inequalities for semilinear elliptic equations
• The Chandrasekhar theory of stellar collapse as the limit quantum mechanics
• Symmetry and related properties via the maximum principle
• Classification of solutions of some nonlinear elliptic equations
• Spectral analysis of pseudodifferential operators
• Spectral theory of the operator \((p^2+m^2)^{1/2}-Ze^2/r\)
• On a conjecture of De Giorgi and some related problems
• Classification of solutions of higher order conformally invariant equations
• On uniqueness of solutions of \(n\)-th order differential equations in conformal geometry
• A classification of solutions of a conformally invariant fourth order equation in \(\mathbb{R}^n\)
• On De Giorgi's conjecture in dimensions 4 and 5
• Moving planes, moving spheres, and a priori estimates.
• One-dimensional symmetry of bounded entire solutions of some elliptic equations
• Maximum principles for the fractional p-Laplacian and symmetry of solutions
• On fractional elliptic equations in Lipschitz sets and epigraphs: regularity, monotonicity and rigidity results
• Classification of nonnegative classical solutions to third-order equations
• Direct methods on fractional equations
• Regularity and classification of solutions to static Hartree equations involving fractional Laplacians
• Classification of positive solutions to fractional order Hartree equations via a direct method of moving planes
• Remark on some conformally invariant integral equations: the method of moving spheres
• Local asymptotic symmetry of singular solutions to nonlinear elliptic equations
• On the Ginzburg-Landau energy with weight
• Uniqueness theorems through the method of moving spheres
• Inequalities for second-order elliptic equations with applications to unbounded domains. I
• The sliding methods for the fractional \(p\)-Laplacian
• Classification of nonnegative solutions to static Schrödinger-Hartree and Schrödinger-Maxwell Equations with combined nonlinearities
• Regularity of flat level sets in phase transitions
• A direct method of moving spheres on fractional order equations
• Boson stars as solitary waves
• A symmetry problem in potential theory
• Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
• Nonrelativistic limit of standing waves for pseudo-relativistic nonlinear Schrödinger equations
• Entire $s$-harmonic functions are affine
• Ground states solutions for a non-linear equation involving a pseudo-relativistic Schrödinger operator
• Uniqueness of Radial Solutions for the Fractional Laplacian
• A concave—convex elliptic problem involving the fractional Laplacian
• Mass concentration phenomenon for inhomogeneous fractional Hartree equations
• Regularity of the obstacle problem for a fractional power of the laplace operator
• Mean field dynamics of boson stars
• Variational Methods for Nonlocal Fractional Problems
• The stability of matter: from atoms to stars
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• Euler Equations, Navier-Stokes Equations and Turbulence
• Entire solutions of semilinear elliptic equations in ℝ³ and a conjecture of De Giorgi
• Nonlinear Analysis - Theory and Methods
• Variational and Topological Methods for Nonlocal Fractional Periodic Equations
• Existence and non-existence results for semilinear elliptic problems in unbounded domains
• A necessary and sufficient condition for the nirenberg problem
• Classification of nonnegative solutions to a bi-harmonic equation with Hartree type nonlinearity
• The Fractional Laplacian
• On the method of moving planes and the sliding method
• Effective dynamics for boson stars
• An Extension Problem Related to the Fractional Laplacian
• Blowup for nonlinear wave equations describing boson stars
• Classification of solutions for an integral equation
• Classification of Nonnegative Solutions to Static Schrödinger--Hartree--Maxwell Type Equations

This page was built for publication: Direct methods for pseudo-relativistic Schrödinger operators