  We consider a class of strongly correlated Fermi systems that exhibit an
interaction-induced flat band pinned to the Fermi surface, and generalize the
Landau strategy to accommodate a flat band and apply the more comprehensive
theory to electron systems of solids. The non-Fermi-liquid behavior that
emerges is compared with relevant experimental data on heavy-fermion metals and
electron-doped high-$T_c$ compounds. We elucidate how heavy-fermion metals have
extremely low superconducting transition temperature $T_c$, its maximum reached
in the heavy-fermion metal CeCoIn$_5$ does not exceed 2.3 K, and explain the
enhancement of $T_c$ observed in high-$T_c$ superconductors. We show that the
coefficient $A_1$ of the $T$-linear resistivity scales with $T_c$, in agreement
with the experimental behavior uncovered in the electron-doped materials. We
have also constructed schematic temperature-doping phase diagram of the copper
oxide superconductor $\rm La_{2-x}Ce_xCuO_4$ and explained the doping
dependence of its resistivity.
