The traps of isolated dust particles under the action of electrostatic, gra
vitational, ion-drag, and neutral collision forces are investigated near th
e boundary of a dusty plasma. It is shown that in the lower sheath (above t
he lower electrode) the particle traps can exist only for the negatively ch
arged particles. The positions of trapped particle are determined by grain
size and forces on it and there are upper and lower critical values for the
trapped particle. In the upper sheath (under the upper electrode) there is
balance force for the positively charged particles but it is not a stable
balance. Still negatively charged particles can be trapped in the upper she
ath. In addition, it was shown that two sized grains are trapped in the sam
e position. (C) 1999 American Institute of Physics. [S1070-664X(99)00105-6]
.