Infinitely many solutions for a class of superlinear Dirac–Poisson system

Abstract This paper is concerned with the nonlinear Dirac–Poisson system − i ∑ k = 1 3 α k ∂ k u + ( V ( x ) + a ) β u + ω u − ϕ u = F u ( x , u ) , − Δ ϕ = 4 π | u | 2 , in R 3 where V is an external potential and F is a superlinear nonlinearity modeling various types of interactions. Existence and multiplicity of stationary solutions are obtained for the system with periodicity condition via variational methods.