The Schrödinger–Poisson equation under the effect of a nonlinear local term

In this paper we study the problem{−Δu+u+λϕu=up,−Δϕ=u2,lim|x|→+∞ϕ(x)=0, where u,ϕ:R3→R are positive radial functions, λ>0λ>0 and 1