Stable branches of a solution for a fermion on domain wall

The case when a fermion occupies an excited nonzero frequency level in the field of domain wall is discussed. It is demonstrated that a solution exists for the coupling constant in the limited interval 1 < g < g (max) a parts per thousand 1.65. It is shown that indeed there are different branches of stable solution for g in this interval. The first one corresponds to a fermion located on the domain wall (1 < g < 4 root 2 pi). The second branch, which belongs to the interval 4 root <= g <= g(max), describes a polarized fermion off the domain wall. The third branch with 1 < g < g (max) describes an excited antifermion in the field of the domain wall.