About the influence of square-root Van Hove singularity on the critical   temperature of high-Tc superconductors
  It is shown that the square-root Van Hove singularity in the density of states (DOS), associated with extended saddle-point features in the electronic spectra of cuprates, leads to a nonmonotonic dependence of Tc on the position of the Fermi level. As the result of cancellation of the DOS divergence in the electron-electron coupling constant, renormalized due to the account of strong-coupling effects, Tc approaches zero when Fermi level touches the bottom of the saddle. The Tc dependence on the doped holes' concentration, obtained in the strong coupling approximation, agrees with experimental data for the overdoped cuprate metal-oxides. 
E. A. Pashitskii, V. I. Pentegov and E. Abraham