A note on a 3-dimensional stationary Schrodinger-Poisson system

In a previous paper we have proved existence of a ground state for a stationary Schr"odinger--Poisson system in the whole space $mathbb{R}^3$ under appropriate assumptions on the data, namely the dopant-density $n^*$ and the effective potential $widetilde V$. In this note we show that the same result remains true under less restrictive hypotheses.