  We study the class of nonlinear Klein-Gordon-Maxwell systems describing a
standing wave (charged matter field) in equilibrium with a purely electrostatic
field. We improve some previous existence results in the case of an homogeneous
nonlinearity. Moreover, we deal with a limit case, namely when the frequency of
the standing wave is equal to the mass of the charged field; this case shows
analogous features of the well known "zero mass case" for scalar field
equations.
