pairing can in some cases give rise to higher $T_{c}$ than in the standard (Migdal-Eliashberg) $BCS$-like theory. Namely, in the $EPI-FSP$ pairing mechanism one has $T_{c}^{(FSP)}=\left\langle V_{epi}(q)\right\rangle
_{q}/4\sim\lambda_{epi}^{(FSP)}/N(E_{F})$ [@Dan-Dol-Kul-Oud] - see below, instead of the $BCS$ dependence $T_{c}^{(BCS)}\sim\Omega e^{-1/\lambda
_{epi}^{(BCS)}}$. Here, $\lambda_{epi}^{(FSP)}$ and $\lambda_{epi}^{(BCS)}$ are the corresponding *mass-independent* $EPI$ coupling constants, where $\Omega$ - is the phonon energy, $N(E_{F})$ - the electronic density of states (per spin) at the Fermi surface. So, even for small $\lambda
_{epi}^{(FSP)}\ll\lambda_{epi}^{(BCS)}$ the case $T_{c}^{(FSP)}>T_{c}^{(BCS)}$ can be in principle realized. We inform the reader in advance, that the $EPI-FSP$ theory predicts also that $T_{c}^{(FSP)}\sim(q_{c}/k_{F})^{d}V_{epi}(0)$, ($d=1,2,3$ is the dimensionality of the system), which means that when $q_{c}\ll k_{F}$ high $T_{c}^{(FSP)}$ is hardly possible in $3D$ systems. However, the detrimental effect of the phase-volume factor $(q_{c}/k_{F})^{d}$ on $T_{c}^{(FSP)}$ can be compensated by its linear dependence on the pairing potential $V_{epi}(0)$. In some favorable materials this competition may lead even to an increase of $T_{c}$. We stress that properties of the superconductors with the $EPI-FSP$ mechanism of pairing are in many respects very different from the standard (BCS-like) superconductors, and it is completely justified to speak about *exotic superconductors*. For instance, the $EPI-FSP$ theory [@Kulic-PhysRep]-[@Dan-Dol-Kul-Oud] predicts, that in 