  Equations of motion are derived for the normal and the anomalous
single-electron density matrices of a Fermi liquid using a time dependent
finite temperature generalized coherent state (GCS) variational ansatz for the
many-body density matrix. Self-consistent equations for the order parameter
$\Delta$ allow to investigate the interplay of Coulomb repulsion and pairing
attraction in homogeneous and inhomogeneous Fermi-liquids with spontaneously
broken symmetry such as high temperature superconductors. The temperature of
the Kosterlitz-Thouless transition to the two-dimensional superfluidity is
calculated.
