Vectorial solutions for a class of Hartree-Fock type systems with the double coupled feature

Ground-State Solutions to a Hartree–Fock Type System with a 3-Lower Nonlinearity

In this paper, ground-state solutions to a Hartree–Fock type system with a critical growth are studied. Firstly, instead of establishing the local Palais–Smale (P.-S.) condition and estimating the mountain-pass critical level, a perturbation method is used to recover compactness obtain the existence of ground-state solutions. To achieve this, an important step is to get the right continuity of the mountain-pass level on the coefficient in front of perturbing terms. Subsequently, depending on the internal parameters of coupled nonlinearities, whether the ground state is semi-trivial or vectorial is proved.

Existence and behavior of minimizers for a class of Hartree–Fock type systems

Standing waves solutions for a coupled Hartree–Fock type nonlocal elliptic system are considered. This nonlocal type problem was considered in the basic quantum chemistry model of small number of electrons interacting with static nucleii which can be approximated by Hartree or Hartree–Fock minimization problems. First, we prove the existence of normalized solutions for different ranges of the positive (attractive case) coupling parameter for the stationary system. Then we extend the results to systems with an arbitrary number of components. Finally, the orbital stability of the corresponding solitary waves for the related nonlocal elliptic system is also considered.

On a planar Hartree–Fock type system

On a planar Hartree–Fock type system involving the $$(2,q)-$$Laplacian in the zero mass case

Hartree-Fock type systems: Existence of ground states and asymptotic behavior