  We propose a solution of the cusp problem in framework of the standard
$\Lambda$CDM cosmology. To do this we describe the linear and nonlinear periods
of halo formation by the entropy function of dark matter particles. This
approach allows us to take into account together the impact of both the
processes of nonlinear relaxation of compressed matter and the small scale
initial velocity perturbations in collapsed halos. We show that such random
velocities lead to the random variations of the density profile of relaxed
halos. As a rule, they suppress the formation of cusp--like halos and favor the
creation of core--like ones. This approach allows us to reproduce observed
rotation curves, to explain their random scatter and deviations from simulated
ones.
