Nonlinear Dirac Equations With Coulomb-type Potentials And Nonlinearities Resonating At Essential Spectrums

We consider the nonlinear Dirac equation-(?).The potential function V satisfies the conditions that the essential spectrum of the Dirac operator--(?)+? +V is(-?,-1]?[1+?)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)=-?/|x|with ?>0 as a special case.The nonlinearity F satisfies the resonance type condition (?).Under some additional conditions on V and F,Finally,we use the pseudo-index theory to prove that the nonlinear Dirac equation has infinitely many solutions.