We consider the nonlinear Dirac equation
The potential function V satisfies the conditions that the essential spectrum of the Dirac operator is and this Dirac operator has infinitely many eigenvalues in (−1, 1) accumulating at 1. This potential function V may change sign in ℝ3 and contains the classical Coulomb potential V (x) = −γ/|x| with γ > 0 as a special case. The nonlinearity F satisfies the resonance-type condition lim. Under some additional conditions on V and F, we prove that this equation has infinitely many solutions.