Existence and multiplicity of the positive normalized solutions to the coupled Hartree-Fock type nonlocal elliptic system

DOI10.1007/S11784-022-01001-3zbMath1505.35142OpenAlexW4310157245MaRDI QIDQ2107610

Yuanyuan Tu, Jun Wang, Qiuping Geng

Publication date: 2 December 2022

Published in: Journal of Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11784-022-01001-3

zbMATH Keywords

variational methodsnormalized solutionsHartree-Fock type nonlocal elliptic system

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Semilinear elliptic equations (35J61) Second-order elliptic systems (35J47)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nodal solutions for the Choquard equation
• Normalized solutions for a system of coupled cubic Schrödinger equations on \(\mathbb R^3\)
• Multiple solutions to a magnetic nonlinear Choquard equation
• A guide to the Choquard equation
• A natural constraint approach to normalized solutions of nonlinear Schrödinger equations and systems
• Symmetry and uniqueness of minimizers of Hartree type equations with external Coulomb potential
• Groundstates of the Choquard equations with a sign-changing self-interaction potential
• Existence and orbital stability of standing waves for nonlinear Schrödinger systems
• Classification of positive solitary solutions of the nonlinear Choquard equation
• The concentration-compactness principle in the calculus of variations. The locally compact case. II
• Odd symmetry of least energy nodal solutions for the Choquard equation
• Standing waves for a coupled nonlinear Hartree equations with nonlocal interaction
• Existence of the normalized solutions to the nonlocal elliptic system with partial confinement
• Solutions of Hartree-Fock equations for Coulomb systems
• Minimax theorems
• Standing waves with prescribed mass for the coupled Hartree-Fock system with partial confinement
• Existence and multiplicity of nontrivial solutions of weakly coupled nonlinear Hartree type elliptic system
• Multiple \(\mathbb {S}^{1}\)-orbits for the Schrödinger-Newton system.
• Standing waves with a critical frequency for nonlinear Choquard equations
• A new rearrangement inequality and its application for \(L^2\)-constraint minimizing problems
• Existence of semiclassical states for a coupled Schrödinger system with potentials and nonlocal nonlinearities
• Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
• Groundstates of nonlinear Choquard equations: Hardy–Littlewood–Sobolev critical exponent
• Uniqueness of positive solutions of the Choquard type equations
• Semi-classical limit for Schrödinger equations with magnetic field and Hartree-type nonlinearities
• Existence of solutions with prescribed norm for semilinear elliptic equations
• Some remarks on Hartree equation
• Global existence of solutions to the Cauchy problem for time-dependent Hartree equations
• Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation
• Multiple positive normalized solutions for nonlinear Schrödinger systems
• Normalized solutions for nonlinear Schrödinger systems
• Spherically-symmetric solutions of the Schrödinger-Newton equations
• ON THE TIME-DEPENDENT HARTREE–FOCK EQUATIONS COUPLED WITH A CLASSICAL NUCLEAR DYNAMICS
• Existence of groundstates for a class of nonlinear Choquard equations
• Least action nodal solutions for the quadratic Choquard equation
• Compactness of Minimizing Sequences in Nonlinear Schrödinger Systems Under Multiconstraint Conditions
• From atoms to crystals: a mathematical journey
• Existence of normalized solutions for the coupled Hartree–Fock type system

This page was built for publication: Existence and multiplicity of the positive normalized solutions to the coupled Hartree-Fock type nonlocal elliptic system