Parton densities in a nucleon

In this paper we re-analyze the situation with the shadowing corrections (SC) in QCD for the proton deep-inelastic structure functions. We reconsider the Glauben-Mueller approach for the SC in deep-inelastic scattering (DIS) and suggest a new non-linear evolution equation, We argue that this equation solves the problem of the SC in the wide kinematic region where alpha(s) kappa = alpha(s) (3 pi alpha(s)/2Q(2)R(2))xG(x, Q(2)) less than or equal to 1. Using the new equation we estimate the value of the SC which turn out to be essential in the gluon deep-inelastic structure function but rather small in F-2(x Q(2)). We claim that the SC in xG(x, Q(2)) is so large that the BFKL Pomeron is hidden under the SC and cannot be seen even in such "hard" processes that have been proposed to test it, We found that the gluon density is proportional to ln(1/x) in the region of very small x, This result means that the gluon density does not reach saturation in the region of applicability of the new evolution equation. It should be confronted with the solution of the GLR equation which leads to saturation, (C) 1998 Published by Elsevier Science B.V.