Ground state sign-changing solution for
Schr\”{o}dinger-Poisson system with critical growth
Abstract
This article is devoted to study the nonlinear
Schr\”{o}dinger-Poisson system with pure power
nonlinearities $$
\left\{\begin{array}{ll}
-\Delta u+u+ \phi
u=|u|^{p-1}u+|u|^4u,
&x\in \mathbb{R}^3,
\\[0.3cm]
-\Delta\phi= u^2, &x\in
\mathbb{R}^3, \end{array}
\right. $$ 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
complements the recent work of Wang et al.
\cite{Wang2019}.