Semirelativistic Choquard equations with singular potentials and general nonlinearities arising from Hartree-Fock theory

DOI10.1016/j.na.2021.112738zbMath1484.35344arXiv2102.02168OpenAlexW3126422877MaRDI QIDQ2074917

Federico Bernini, Bartosz Bieganowski, Simone Secchi

Publication date: 11 February 2022

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.02168

zbMATH Keywords

fractional operatorssign-changing nonlinearitiesChoquard equationHartree-Fock theory

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Variational methods applied to PDEs (35A15) Fractional derivatives and integrals (26A33) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Variational methods for second-order elliptic equations (35J20) Fractional partial differential equations (35R11)

Related Items (3)

Asymptotic decay of solutions for sublinear fractional Choquard equations ⋮ On nonlinear fractional Schrödinger equations with indefinite and Hardy potentials ⋮ On the ground states for the X‐ray free electron lasers Schrödinger equation

Cites Work

• Hitchhiker's guide to the fractional Sobolev spaces
• Existence of ground states for nonlinear, pseudo-relativistic Schrödinger equations
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• Uniqueness of ground states for pseudorelativistic Hartree equations
• Hartree-Fock theory for pseudorelativistic atoms
• Nonlinear ground state representations and sharp Hardy inequalities
• Relativistic stability of matter. I
• The Chandrasekhar theory of stellar collapse as the limit quantum mechanics
• The stability and instability of relativistic matter
• Existence of solutions for a semirelativistic Hartree equation with unbounded potentials
• The fractional Schrödinger equation with Hardy-type potentials and sign-changing nonlinearities
• Existence and nonlinear stability of stationary states for the semi-relativistic Schrödinger-Poisson system
• Multiple solutions to a nonlinear curl-curl problem in \({\mathbb{R}}^3\)
• Semiclassical analysis for pseudo-relativistic Hartree equations
• Existence of groundstates for a class of nonlinear Choquard equations in the plane
• Choquard-type equations with Hardy-Littlewood-Sobolev upper-critical growth
• The semirelativistic Choquard equation with a local nonlinear term
• Ground states for pseudo-relativistic Hartree equations of critical type
• Boson stars as solitary waves
• Dynamical collapse of white dwarfs in Hartree- and Hartree-Fock theory
• Ground states of nonlinear Schrödinger equations with sum of periodic and inverse-square potentials
• Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
• Multiple solutions of the quasirelativistic Choquard equation
• Mean field dynamics of boson stars
• The stability of matter: from atoms to stars
• Solutions to a nonlinear Maxwell equation with two competing nonlinearities in $\mathbb{R}^3$
• Ground states for the pseudo-relativistic Hartree equation with external potential
• On fractional Choquard equations
• Existence of groundstates for a class of nonlinear Choquard equations
• Effective dynamics for boson stars
• Unnamed Item
• Unnamed Item

This page was built for publication: Semirelativistic Choquard equations with singular potentials and general nonlinearities arising from Hartree-Fock theory