Existence of non-trivial solutions for nonlinear fractional Schrödinger-Poisson equations

We study the nonlinear fractional Schrödinger-Poissonequation (−Δ)su+u+ϕu=f(x,u),inR3,(−Δ)tϕ=u2,inR3,where s,t∈(0,1], 2t+4s>3. Under some assumptions on f, we obtain the existence of non-trivial solutions. The proof is based on the perturbation method and the mountain pass theorem.