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

This paper is concerned with the nonlinear Dirac-Poisson system −i∑k=13αk∂ku+(V(x)+a)βu+ωu−ϕu=Fu(x,u),−Δϕ=4π|u|2,inR3where 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.