Stationary periodic solutions to Nonlinear Dirac equations with non-coercive potentials

We obtain periodic solutions for nonlinear Dirac equations with a nonlinear term that is not necessarily coercive.This amounts to study the equation on a three-dimensional torus.The Palais-Smale condition is enhanced by involving a coercive perturbation.Uniform estimates for the critical levels as well as the Sobolev norms for the perturbed solutions are obtained, making it possible to pass to a limit which gives a nontrivial solution.