  In this publication a microscopic theory for the coupling of intrinsic
Josephson oscillations in layered superconductors with longitudinal
c-axis-phonons is developed. It is shown that the influence of lattice
vibrations on the c-axis transport can be fully described by introducing an
effective longitudinal dielectric function. Resonances in the
I-V-characteristic appear at van Hove singularities of both acoustical and
optical longitudinal phonon branches. This provides a natural explanation of
the recently discovered subgap structures in the I-V-characteristic of highly
anisotropic cuprate superconductors. The effect of the phonon dispersion on the
damping of these resonances and the coupling of Josephson oscillations in
different resistive junctions due to phonons are discussed in detail.
