  We show that the nonlinear corrections to the longitudinal structure function
can be tamed the singularity behavior at low x values, with respect to GLR-MQ
equations. This approach can determined the shadowing longitudinal structure
function based on the shadowing corrections to the gluon and singlet quark
structure functions. Comparing our results with HERA data show that at very low
x this behavior completely tamed by these corrections.
