Green function of fermions in 2D superconducting Frohlich model with inhomogeneous order parameter

The fermion Green function and spectral characteristics for the 2D Frohlich model of superconductivity at static fluctuations in the phase of the order parameter are calculated. The results demonstrate strongly non-Fermi-liquid properties of the system at finite temperatures and relate with the pseudogap behavior of high-$T_c$ superconductors at relatively small charge carrier densities.