  We consider competition of Kondo effect and s-wave superconductivity in heavy
fermion and mixed valence superconductors, using the phenomenological approach
for the periodic Anderson model. Similar to the well known results for
single-impurity Kondo effect in superconductors, we have found principal
possibility of a re-entrant regime of the superconducting transition
temperature, $T_c$, in heavy fermion superconductors in a narrow range of model
parameters and concentration of f-electrons. Suppression of $T_c$ in mixed
valence superconductors is much weaker. Our theory has most validity in the
low-temperature Fermi liquid regime, without re-entrant behavior of $T_c$. To
check its applicability, we performed the fit for the $x$-dependence of $T_c$
in Ce$_{1-x}$La$_x$Ru$_3$Si$_2$ and obtained an excellent agreement with the
experimental data, although no re-entrance was found in this case. Other
experimental data are discussed in the light of our theoretical analysis. In
particular, we compare temperatures of the superconducting transition for some
known homologs, i.e., the analog periodic lattice compounds with and without
f-elements. For a few pairs of homologs superconductivity exists only in the
heavy fermion materials, thus confirming uniqueness of superconductivity
mechanisms for the latter. We suggest that for some other compounds the value
of $T_c$ may remain of the same order in the two homologs, if superconductivity
originates mainly on some light Fermi surface, but induces sizable
superconducting gap on another Fermi surface,for which hybridization or other
heavy fermion effects are more significant.
