On the existence of solutions for the Schrödinger–Poisson equations

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