Reverse order laws for the Drazin inverses

This paper is to present some equivalent conditions concerning the reverse order law (PQ)D=QDPD(PQ)D=QDPD for the Drazin invertible operators P and Q   with partial commutative properties [P,PQ]=0[P,PQ]=0 or [Q,PQ]=0[Q,PQ]=0 or [P,PQQD]=0[P,PQQD]=0 or [Q,PPDQ]=0[Q,PPDQ]=0.