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

Abstract

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