Ground State Sign-Changing Solution for Schrödinger-Poisson System with Critical Growth

Abstract

This article is devoted to study the nonlinear Schrödinger-Poisson system with pure power nonlinearities $$\begin{aligned} \left\{ \begin{array}{ll} -\Delta u+u+ \phi u=|u|^{p-1}u+|u|^4u, &{}x\in {\mathbb {R}}^3, \\ -\Delta \phi = u^2, &{}x\in {\mathbb {R}}^3, \end{array} \right. \end{aligned}$$ where $$4< p<5$$ . By employing constraint variational method and a variant of the classical deformation lemma, we show the existence of one ground state sign-changing solution with precisely two nodal domains, which improves and generalizes the existing results by Wang, Zhang and Guan (J. Math. Anal. Appl. 479 (2019), 2284–2301).