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We consider competition of Kondo effect and s-wave superconductivity in heavyfermion and mixed valence superconductors, using the phenomenological approachfor the periodic Anderson model. Similar to the well known results forsingle-impurity Kondo effect in superconductors, we have found principalpossibility of a re-entrant regime of the superconducting transitiontemperature, $T_c$, in heavy fermion superconductors in a narrow range of modelparameters and concentration of f-electrons. Suppression of $T_c$ in mixedvalence superconductors is much weaker. Our theory has most validity in thelow-temperature Fermi liquid regime, without re-entrant behavior of $T_c$. Tocheck 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 theexperimental data, although no re-entrance was found in this case. Otherexperimental data are discussed in the light of our theoretical analysis. Inparticular, we compare temperatures of the superconducting transition for someknown homologs, i.e., the analog periodic lattice compounds with and withoutf-elements. For a few pairs of homologs superconductivity exists only in theheavy fermion materials, thus confirming uniqueness of superconductivitymechanisms for the latter. We suggest that for some other compounds the valueof $T_c$ may remain of the same order in the two homologs, if superconductivityoriginates mainly on some light Fermi surface, but induces sizablesuperconducting gap on another Fermi surface,for which hybridization or otherheavy fermion effects are more significant.Comment: 11 pages, 4 figures, pd

Competition between phonon superconductivity and Kondo screening in mixed valence and heavy fermion compounds