Analysis of the Longitudinal Structure Function F_L from the Non-linear Regge Gluon Density Behavior at Low-x

The longitudinal structure function with shadowing correction according to the nonlinear effects of the gluon density behavior at low x is considered. The solution of the GLR-MQ evolution equation for the gluon density shows that the F_L^g(x,Q²) behavior can be tamed by the singularity at low x values. Comparing our results with H1 data at R=4 GeV⁻¹ shows that at very low x this behavior is completely tamed by taking shadowing correction into account.