  The possibility of non-s-wave superconductivity induced by phonons is
investigated using a simple model that is inspired by Sr$_2$RuO$_4$. The model
assumes a two-dimensional electronic structure, a two-dimensional
spin-fluctuation spectrum, and three-dimensional electron-phonon coupling.
Taken separately, each interaction favors formation of spin-singlet pairs (of s
symmetry for the phonon interaction and d$_{x^2-y^2}$ symmetry for the spin
interaction), but in combination, a variety of more unusual singlet and triplet
states are found, depending on the interaction parameters. This may have
important implications for Sr$_2$RuO$_4$, providing a plausible explanation of
how the observed spin fluctuations, which clearly favor d$_{x^2-y^2}$ pairing,
may still be instrumental in creating a superconducting state with a different
(e.g., p-wave) symmetry. It also suggests an interpretation of the large
isotope effect observed in Sr$_2$RuO$_4$. These results indicate that phonons
could play a key role in establishing the order-parameter symmetry in
Sr$_2$RuO$_4$, and possibly in other unconventional superconductors.
