Existence and asymptotics of ground states to the nonlinear Dirac equation with Coulomb potential

DOI10.3233/ASY-211748zbMath1498.35459OpenAlexW4200445770MaRDI QIDQ5040041

Wen Zhang, Jian Zhang, Tian-Fang Wang

Publication date: 11 October 2022

Published in: Asymptotic Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3233/asy-211748

zbMATH Keywords

Dirac equationCoulomb potentialground state solutionsasymptotic property

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Cites Work

• Unnamed Item
• Existence of ground state solutions to Dirac equations with vanishing potentials at infinity
• Semi-classical limits of ground states of a nonlinear Dirac equation
• Solutions of Schrödinger equations with inverse square potential and critical nonlinearity
• Ground state solutions for Hamiltonian elliptic system with inverse square potential
• On an elliptic problem with critical exponent and Hardy potential
• Solutions for semilinear elliptic equations with critical exponents and Hardy potential
• The nonlinear Dirac equation in Bose-Einstein condensates: foundation and symmetries
• Periodic nonlinear Schrödinger equation with application to photonic crystals
• Existence of stationary states for nonlinear Dirac equations
• Existence of excited states for a nonlinear Dirac field
• The concentration-compactness principle in the calculus of variations. The locally compact case. II
• Infinitely many solutions for an elliptic problem involving critical Sobolev growth and Hardy potential
• Semi-classical ground states concentrating on the nonlinear potential for a Dirac equation
• Solutions of a nonlinear Dirac equation with external fields
• Ground state solutions for some indefinite variational problems
• Existence of localized solutions for a classical nonlinear Dirac field
• A note on the sign-changing solutions to elliptic problems with critical Sobolev and Hardy terms.
• An overview on linear and nonlinear Dirac equations
• An infinite sequence of localized semiclassical bound states for nonlinear Dirac equations
• On the concentration of semiclassical states for nonlinear Dirac equations
• Elliptic problems with critical exponents and Hardy potentials.
• Stationary states of the nonlinear Dirac equation: A variational approach
• Minimax theorems
• Existence of solutions for a class of nonlinear Schrödinger equations with potential vanishing at infinity
• Generalized linking theorem with an application to a semilinear Schrödinger equation
• Existence and exponential decay of ground-state solutions for a nonlinear Dirac equation
• Semiclassical states of nonlinear Dirac equations with degenerate potential
• Ground states for planar Hamiltonian elliptic systems with critical exponential growth
• Concentration behavior of semiclassical solutions for Hamiltonian elliptic system
• Localized concentration of semi-classical states for nonlinear Dirac equations
• On Schrödinger operators with multipolar inverse-square potentials
• Solutions of nonlinear Dirac equations
• Non-Nehari manifold method for asymptotically periodic Schrödinger equations
• Ground states of nonlinear Schrödinger equations with sum of periodic and inverse-square potentials
• Existence of standing waves for Dirac fields with singular nonlinearities
• Schrödinger semigroups
• Nonlinear Spinor Field
• Deformation theorems on non-metrizable vector spaces and applications to critical point theory
• Variational methods in relativistic quantum mechanics
• STATIONARY STATES OF NONLINEAR DIRAC EQUATIONS WITH GENERAL POTENTIALS
• A global compactness result for singular elliptic problems involving critical Sobolev exponent
• AN ASYMPTOTICALLY PERIODIC SCHRÖDINGER EQUATION WITH INDEFINITE LINEAR PART
• Elliptic Equations with Multi-Singular Inverse-Square Potentials and Critical Nonlinearity
• Ground state solutions for nonperiodic Dirac equation with superquadratic nonlinearity

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