Existence and multiplicity of solutions of Schrodinger-Poisson systems with radial potentials

In this paper, we deal with the nonlinear Schrodinger-Poisson system -Delta u + V(vertical bar x vertical bar)u + phi u = lambda Q(vertical bar x vertical bar)f(u) in R-3, -Delta phi = u(2) in R-3, where lambda > 0, V and Q are radial functions, which can be vanishing or coercive at infinity. With assumptions on f just in a neighbourhood of the origin, existence and multiplicity of non-trivial radial solutions are obtained via variational methods. In particular, if f is sublinear and odd near the origin, we obtain infinitely many solutions of (SP)(lambda) for any lambda > 0.