On the Existence of Infinitely Many Solutions for Nonlinear Klein–Gordon–Maxwell Systems Under Weak Nonlinearity Conditions

In this paper, the existence of infinitely many nontrivial solutions to a class of nonlinear Klein-Gordon-Maxwell systems in R 3 is investigated, where the nonlinearity is either superquadratic or exhibits combined growth (i.e., both subquadratic and superquadratic behavior at infinity).The potential V (x) is allowed to be neither coercive nor uniformly positive.By employing variational methods, in particular the symmetric mountain pass theorem and the dual fountain theorem, new existence results are established under significantly weaker assumptions on the nonlinearity, without requiring the classical Ambrosetti-Rabinowitz condition.The obtained results extend and improve several known results in the literature and are applicable to a broader class of nonlinearities.