  We show that it is possible to use hard-Pomeron behavior to the gluon
distribution and singlet structure function at low $x$. We derive a
second-order independent differential equation for the gluon distribution and
the singlet structure function. In this approach, both singlet quarks and
gluons have the same high-energy behavior at small $x$. These equations are
derived from the next-to-leading order DGLAP evolution equations. All results
can be consistently described in the framework of perturbative QCD, which shows
an increase of gluon distribution and singlet structure functions as $x$
decreases.
