Ground state solutions for an asymptotically 2-linear Schrödinger-Poisson system

In this paper, we study the following Schrödinger-Poissonsystem −Δu+u+ϕu=g(u),inR3,−Δϕ=u2,inR3,where g is a continuous function and superlinear at zero, and g(t)t≥3G(t)≥0 with G(t)=∫0tg(s)ds, t∈R. We establish the existence of ground state solutions, by using a condition lim|t|→∞g(t)|t|2=ν with 1898πS(32π3)53<ν<+∞, instead of the usual 2-superlinear condition lim|t|→∞G(t)|t|3=+∞.