  We investigate galaxy formation in models with dark matter (DM) constituted
by sterile neutrinos. Given their large parameter space, defined by the
combinations of sterile neutrino mass $m_{\nu}$ and mixing parameter
$\sin^2(2\theta)$ with active neutrinos, we focus on models with $m_{\nu}=7$
keV, consistent with the tentative 3.5 keV line detected in several X-ray
spectra of clusters and galaxies. We consider i) two resonant production models
with $\sin^2(2\theta)=5\,10^{-11}$ and $\sin^2(2\theta)=2\,10^{-10}$, to cover
the range of mixing parameter consistent with the 3.5 keV line; ii) two
scalar-decay models, representative of the two possible cases characterizing
such a scenario: a freeze-in and a freeze-out case. We also consider thermal
Warm Dark Matter with particle mass $m_X=3$ keV. Using a semi-analytic model,
we compare the predictions for the different DM scenarios with a wide set of
observables. We find that comparing the predicted evolution of the stellar mass
function, the abundance of satellites of Milky Way-like galaxies, and the
global star formation history of galaxies with observations does not allow to
disentangle the effects of the baryonic physics from those related to the
different DM models. On the other hand, the distribution of the stellar-to-halo
mass ratios, the abundance of faint galaxies in the UV luminosity function at
$z\gtrsim 6$, and the specific star formation and age distribution of local,
low-mass galaxies constitute potential probes for the considered DM scenarios.
We discuss how next observations with upcoming facilities will enable to rule
out or to strongly support DM models based on sterile neutrinos.
