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 ≈ 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 < sqrt[4]{{2pi }})). The second branch, which belongs to the interval (sqrt[4]{{2pi }} leqslant g leqslant 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.