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Ground state sign-changing solution for Schr\”{o}dinger-Poisson system with critical growth
  • Ying Wang ,
  • Ziheng Zhang,
  • Rong Yuan
Ying Wang
Beijing Normal University
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Ziheng Zhang
Tiangong University
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Rong Yuan
Beijing Normal University
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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}.