  Magnetic impurities placed in the superconductor can lead to emergence of the
Yu-Shiba-Rusinov bound states. Coupling between the impurity and the substrate
depends on density of states (DOS) at the Fermi level and can be tuned by DOS
singularities. In this paper, we study the role of DOS singularities using the
real space Bogoliubov-de Gennes equations for chosen lattice models. To uncover
the role of these singularities (Dirac point, van Hove singularity, or the flat
band), we study honeycomb, kagome, and Lieb lattices. We show that the
properties of the Shiba state strongly depends on the type of lattice.
Nevertheless some behaviors are generic, e.g. dependence of the critical
magnetic coupling on the DOS at the Fermi level. However, the Shiba states
realized in the Lieb lattice exhibit extraordinary properties, which can be
explained by the presence of a few nonequivalent sublattices. Depending on the
location of the magnetic impurity in the chosen sublattice, the value of
critical magnetic coupling $J_\text{c}$ can be reduced or enhanced when the
flat band is located at the Fermi level. In this context, we also present
differences in the local DOS and coherence lengths for different sublattices in
the Lieb lattice.
