Least energy radial sign-changing solution for the Schrödinger–Poisson system in R³ under an asymptotically cubic nonlinearity

In this paper we consider the following Schrödinger–Poisson system in the whole R³, {−Δu+u+λϕu=f(u) in R³,−Δϕ=u² in R³, where λ>0 and the nonlinearity f is “asymptotically cubic” at infinity. This implies that the nonlocal term ϕu and the nonlinear term f(u) are, in some sense, in a strict competition. We show that the system admits a least energy sign-changing and radial solution obtained by minimizing the energy functional on the so-called nodal Nehari set.