Comment on `Solutions to quasi-relativistic multi-configurative Hartree-Fock equations in quantum chemistry', by C. Argaez & M. Melgaard

In a recent paper published in Nonlinear Analysis: Theory, Methods & Applications, C. Argaez and M. Melgaard studied excited states for pseudo-relativistic multi-configuration methods. Their paper follows a previous work of mine in the non-relativistic case (Arch. Rat. Mech. Anal., 171, 2004). The main results of the paper of C. Argaez and M. Melgaard are correct, but the proofs are both wrong and incomplete.