  The sterile neutrino is a viable dark matter candidate that can be produced
in the early Universe via non-equilibrium processes, and would therefore
possess a highly non-thermal spectrum of primordial velocities. In this paper
we analyse the process of structure formation with this class of dark matter
particles. To this end we construct primordial dark matter power spectra as a
function of the lepton asymmetry, $L_6$, that is present in the primordial
plasma and leads to resonant sterile neutrino production. We compare these
power spectra with those of thermally produced dark matter particles and show
that resonantly produced sterile neutrinos are much colder than their thermal
relic counterparts. We also demonstrate that the shape of these power spectra
is not determined by the free-streaming scale alone. We then use the power
spectra as an input for semi-analytic models of galaxy formation in order to
predict the number of luminous satellite galaxies in a Milky Way-like halo. By
assuming that the mass of the Milky Way halo must be no more than
$2\times10^{12}M_{\odot}$ (the adopted upper bound based on current
astronomical observations) we are able to constrain the value of $L_6$ for
$M_s\le 8$~keV. We also show that the range of $L_6$ that is in best agreement
with the 3.5~keV line (if produced by decays of 7~keV sterile neutrino)
requires that the Milky Way halo has a mass no smaller than
$1.5\times10^{12}M_{\odot}$. Finally, we compare the power spectra obtained by
direct integration of the Boltzmann equations for a non-resonantly produced
sterile neutrino with the fitting formula of Viel~et~al. and find that the
latter significantly underestimates the power amplitude on scales relevant to
satellite galaxies.
