Oscillatory solutions of the BCS gap equation

When the Frohlich interaction is introduced in the BCS gap equation instead of Cooper's simplified form, and the electron-phonon coupling constant λ is negative, oscillatory solutions are obtained for the gap function Δ(ε). We argue that these oscillatory solutions may be correct mathematically for a phonon or exciton spectrum which approximates an Einstein spectrum. We also argue that these oscillatory solutions may be relevant to the high-T_c cuprates.