  To extend the applicability of density functional theory for superconductors
(SCDFT) to systems with significant particle-hole asymmetry, we construct a new
exchange-correlation kernel entering the gap equation. We show that the kernel
is numerically stable and does not diverge even in the low temperature limit.
Solving the gap equation for model systems with the present kernel analytically
and numerically, we find that the asymmetric component of electronic density of
states, which has not been considered with the previous kernel, systematically
decreases transition temperature (Tc). We present a case where the decrease of
Tc amounts to several tens of percent.
