QCD predictions for the behavior of the gluon distribution at small<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>x</mml:mi></mml:math>

The very-small-$x$ behavior of the gluon distribution in a proton is obtained by solving the Lipatov equation with the nonlinear shadowing term incorporated. We find, with decreasing $x$, the emergence of an ${x}^{\ensuremath{-}\ensuremath{\lambda}}$ behavior and the eventual taming of this singular behavior by the shadowing term. We compare our dynamically generated gluon distribution with (i) the results of a recent next-to-leading order QCD structure function analysis which incorporated both a singular ${x}^{\ensuremath{-}\frac{1}{2}}$ behavior and shadowing corrections, and (ii) the double-leading-logarithm approximation. We formulate the semiclassical approximation of the Lipatov equation, with and without shadowing contributions, in order to compare with earlier analyses based on this approximation.