Problems of cosmology on small scales of the Universe

Six challenges for the standard cosmological model $\Lambda$CDM are listed, which arise when comparing theoretical predictions with observational data on scales of ~1 Mpc. Different parameters of luminous and dwarf galaxies in the local sphere with a radius of 12 Mpc are presented. The average densities of stellar matter and dark matter are reproduced depending on a distance in the Local volume. Observational data on distribution of angular momentum of nearby galaxies are considered. A comparison of the dark matter mass estimates for systems of galaxies based on motions of their internal (virialized) members and neighboring galaxies is given. The reasons for the low derived value of the dark matter density, $\Omega_m = 0.08\pm0.02$, in the Local Universe with respect to the global value $\Omega_m = 0.30\pm0.02$ are discussed