  Classical results concerning Klein-Gordon-Maxwell type systems are shortly
reviewed and generalized to the setting of mixed local-nonlocal operators,
where the nonlocal one is allowed to be nonpositive definite according to a
real parameter. In this paper, we provide a range of parameter values to ensure
the existence of solitary (standing) waves, obtained as Mountain Pass critical
points for the associated energy functionals in two different settings, by
considering two different classes of potentials: constant potentials and
continuous, bounded from below, and coercive potentials.
