The number of nodal solutions for the Schrödinger–Poisson system under the effect of the weight function

In this paper, we study the multiplicity of two spikes nodal solutions for a nonautonomous Schrödinger–Poisson system with nonlinearity \begin{document}$ f(x)\vert u\vert ^{p-2}u(2<p<6) $\end{document} in id="M2">\begin{document}$ \mathbb{R}^{3} $\end{document}. By assuming that weight function id="M3">\begin{document}$ f\in C(\mathbb{R}^{3},\mathbb{R}^{+}) has id="M4">\begin{document}$ m maximum points id="M5">\begin{document}$ $\end{document}, conclude such admits id="M6">\begin{document}$ m^{2} distinct solutions, each which exactly domains. The proof is based on natural constraint approach developed by us as well generalized barycenter map.