  The problem of a fermion subject to a general scalar potential in a
two-dimensional world is mapped into a Sturm-Liouville problem for nonzero
eigenenergies. The searching for possible bounded solutions is done in the
circumstance of power-law potentials. The normalizable zero-eigenmode solutions
are also searched. For the specific case of an inversely linear potential,
which gives rise to an effective Kratzer potential, exact bounded solutions are
found in closed form. The behaviour of the upper and lower components of the
Dirac spinor is discussed in detail and some unusual results are revealed.
