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

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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).

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Authors and Affiliations

  1. School of Mathematical Sciences, Tiangong University, Tianjin, 300387, People’s Republic of China

    Ziheng Zhang

  2. Laboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People’s Republic of China

    Ying Wang & Rong Yuan

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  1. Ziheng Zhang
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  2. Ying Wang
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  3. Rong Yuan
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Correspondence to Ziheng Zhang.

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Zhang, Z., Wang, Y. & Yuan, R. Ground State Sign-Changing Solution for Schrödinger-Poisson System with Critical Growth. Qual. Theory Dyn. Syst. 20, 48 (2021). https://doi.org/10.1007/s12346-021-00487-5

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