  We investigate the possible superconducting instabilities of strongly
correlated electron materials using a generalization of linear response theory
to external pairing fields depending on frequency. We compute a pairing
susceptibility depending on two times, allowing us to capture dynamical pairing
and in particular odd-frequency solutions. We first benchmark this method on
the attractive one-band Hubbard model and then consider the superconductivity
of strontium ruthenate Sr$_2$RuO$_4$ within single-site dynamical mean-field
theory, hence restricting ourselves to pairing states which are momentum
independent in the orbital basis. The symmetry of the superconducting order
parameter of this material is still debated, and local odd-frequency states
have been proposed to explain some experimental discrepancies. In the
temperature range studied, we find that the leading eigenvectors are
odd-frequency intra-orbital spin-triplet states, while the eigenvectors with
the highest predicted transition temperature correspond to even-frequency
intra-orbital spin-singlet states. The latter include a state with $d$-wave
symmetry when expressed in the band basis.
