Klein–Gordon–Maxwell equations driven by mixed local–nonlocal operators

Classical results concerning Klein–Gordon–Maxwell type sys- tems 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 func- tionals in two different settings, by considering two different classes of potentials: constant potentials and continuous, bounded from below, and coercive potentials.