The equilibrium, stability, and trapping of dust particles associated with
vertical motions in the plasma sheath and presheath are calculated, taking
into account the dependence of the variables (such as dust charge, ion flow
velocity, etc.) on the local position in the sheath or presheath region of
a collisional plasma with an ionization source. It is demonstrated that an
increase of the rate of ionization considerably influences the equilibrium
positions of dust grains, shifting them toward the electrode as well as in
creasing the maximum possible (equilibrium) levitation grain size.