On the existence of solutions for the Schrödinger–Poisson equations

In this paper, we are concerned with the system of Schrödinger–Poisson equationsequation(*){−Δu+V(x)u+ϕu=f(x,u),in R3,−Δϕ=u2,in R3. Under certain assumptions on V and f, the existence and multiplicity of solutions for (*) are established via variational methods.