  We have studied the normal and superconductive state characteristics
(resistivity, Hall coefficient, heat capacity and magnetization) of model
strongly correlated electronic systems LuxZr1-xB12 with cooperative Jahn-Teller
instability of the boron rigid cage and with dynamic charge stripes. It was
found that these metals are s-wave dirty limit superconductors with a small
mean free path of charge carriers l = 5 - 140 A and with a Cooper pair size
changing non-monotonously in the range 450 - 4000 A. The parent ZrB12 and LuB12
borides are type-I superconductors, and Zr to Lu substitution induces a type-I
- type-II phase transition providing a variation of the Ginzburg-Landau-Maki
parameter in the limits 0.65 < kappa1,2 < 6. We argue in favor of the two-band
scenario of superconductivity in LuxZr1-xB12 with gap values Delta_1 ~ 14 K and
Delta_2 ~ 6 - 8 K, with pairing corresponding to strong coupling limit
(lambda_e-ph ~ 1) in the upper band, and to weak coupling (lambda_e-ph ~ 0.1 -
0.4) in the lower one. A pseudogap Delta_ps-gap ~ 60 - 110 K is observed in
LuxZr1-xB12 above Tc. We discuss also the possibility of anisotropic
single-band superconductivity with stripe-induced both pair-breaking and
anisotropy, and analyze the origin of unique enhanced surface superconductivity
detected in these model compounds.
