Oscillatory gap superconductivity

We show that a purely-repulsive potential gives rise to a BCS-like condensed state with a gap function Δ(ε{lunate}) that oscillates with ε{lunate}. This superconducting state has a lower binding energy than the Stoner magnetic state. A small excitonic interaction increases the binding energy of the superconducting state above that of the magnetic state. This superconducting state is stable in the presence of a large Coulomb repulsion. Electron-phonon coupling of moderate strength greatly increases the value of Δ(0). A large variety of experimental properties of the cuprate superconductors are in accord with the predictions of the oscillatory gap model.