Multiple normalized solutions for the coupled Hartree–Fock system with upper critical exponent

In the present paper, we are concerned with the existence and multiplicity of normalized solutions of coupled Hartree–Fock system with upper critical exponent and lower power perturbation. This type system arises from the basic quantum chemistry model of small number of electrons interacting with static nuclei which can be approximated by Hartree or Hartree–Fock minimization problems. First, by constraint manifold methods and refined energy estimates, we prove the existence of ground and bound states normalized solutions for critical Hartree–Fock system. Then the precise asymptotic behaviors of two normalized solutions are also obtained. Finally, we discuss the orbital stability and finite time blow-up of the associated solitary wave solutions.