In previous papers the relativistic corrections for the mass and potential energy to one-nucleon levels and the significant terms of the relativistic corrections for the mass of nucleons were obtained. In this paper the mathematical problems of semi-relativistic model are considered. The semi-relativistic single-particle equation is a differential equation of the fourth-order and it can be reduced to the integral--differential equations. The general solution of this equation must be expressed by the superposition of the four linearly independent solutions. Developing the modified method of Lagrange's and the multiplicative perturbation theory we obtained the integral--differential equations for the wave functions with usual asymptotic at the origin r^L+1 and unusual r^L+3, r^-L+2. The wave functions with asymptotic at the origin r^L+3 must be used when the singular realistic nuclear potentials are included.

PACS numbers: 21.60.-n, 21.60.Cs