Existence and multiplicity results for stationary solutions of the Dirac equation \(-i\partial _{t}\psi =ic\hslash \sum_{k=1}^{3}a_{k}\partial _{k}\psi -mc^{2}\beta \psi +\nabla _{\psi }G(x,\psi )\) are established via variational method. The associated Lagrangian functional is strongly indefinite and the Palais-Smale (PS) condition is not satisfied. Some recent saddle point theorems with Cerami type (PS) condition are applied to the considered functional.