Existence of nontrivial distributional solutions for a class of Schrödinger-Poisson system with Sobolev critical nonlinearity and zero mass

This paper studies a class of Schrödinger-Poisson system in R3 with Sobolev critical nonlinearity and zero mass −Δu+ϕu=λf(u)+u5,x∈R3;−Δϕ=u2,x∈R3, where λ is a positive parameter and f is a continuous function defined on R with some suitable assumptions. One nontrivial distributional solution is obtained by a combination of variational methods and perturbation method.