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In this paper we consider the following Schr\"odinger-Poisson system in thewhole $\mathbb R^{3}$, \begin{equation*}  \left\{  \begin{array}{ll}  -\Delta u+u+ \lambda \phi u=f(u) &\text{ in } \mathbb R^3,  -\Delta \phi= u^2 &\text{ in } \mathbb R^3,  \end{array}  \right. \end{equation*} where $\lambda>0$ and the nonlinearity $f$ is"asymptotically cubic" at infinity. This implies that the nonlocal term $\phiu$ 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 solutionobtained by minimizing the energy functional on the so-called {nodal Nehariset).

Least energy radial sign-changing solution for the Schr\"oinger-Poisson system in r3 under an asymptotically cubic nonlinearity