  Exact solutions of two-particle relativistic equations of quantum field
theory describing the scattering $s$-states and the bound $s$-states are found
in the cases of delta-shell potential and superposition of delta-shell
potentials. Some properties of obtained relativistic wave functions, scattering
amplitudes and quantization conditions are investigated. The resonance
character of scattering processes is demonstrated by the behavior of
amplitudes. It is shown that the non-relativistic limits of these relativistic
values coincide with respective non-relativistic ones obtained from the
Schr\"{o}dinger equation.
