Periodic solutions to a nonlinear Dirac-Klein-Gordon system with concave and convex nonlinearities

Using the variational method, we study the existence and multiplicity of periodic solutions to nonlinear Dirac-Klein-Gordon systems with two types of nonlinearities. Both the Dirac field and the Klein–Gordon field considered here are general nonlinear fields, different from previously considered models. Moreover, results for the regularity of the solutions are given. In addition, we obtain the soliton-like solution of Dirac-Klein-Gordon systems by approximation of periodic solutions.