Existence of normalized solutions for the coupled Hartree–Fock type system

Abstract

Abstract 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.

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