In this paper, we are interested in the global existence result for a class of Klein–Gordon equations, particularly unified time decay concerning possibly vanishing mass parameter. We give first rigorous proof problem, which relies on both flat foliation and hyperboloidal Minkowski spacetime. To take advantage foliations, an iteration procedure is used.

In the paper we consider the nonexistence of global solutions of the Cauchy problem for coupled Klein-Gordon equations of the form

In this paper we prove the existence of a ground state solution for the nonlinear Klein-Gordon-Maxwell equations in the electrostatic case.