  We consider a model of electrons at zero temperature, with a repulsive
interaction which is a function of the energy transfer. Such an interaction can
arise from the combination of electron-electron repulsion at high energies and
the weaker electron-phonon attraction at low energies. As shown in previous
works, superconductivity can develop despite the overall repulsion due to the
energy dependence of the interaction, but the gap $\Delta(\omega)$ must change
sign at some (imaginary) frequency $\omega_0$ to counteract the repulsion.
However, when the constant repulsive part of the interaction is increased, a
quantum phase transition towards the normal state occurs. We show that, as the
phase transition is approached, $\Delta$ and $\omega_0$ must vanish in a
correlated way such that $1/|\log[\Delta(0)]| \sim \omega_0^2$. We discuss the
behavior of phase fluctuations near this transition and show that the
correlation between $\Delta(0)$ and $\omega_0$ locks the phase stiffness to a
non-zero value.
