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Existence and Multiplicity of Solutions for a Fractional Schrödinger–Poisson System with Subcritical or Critical Growth

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Abstract

In this paper, we study the existence of positive ground state solutions and infinitely many geometrically distinct solutions for the following fractional Schrödinger–Poisson system

$$\begin{aligned} {\left\{ \begin{array}{ll} (-\Delta )^s u+V(x)u+\phi u=f(x,u), &{} \text{ in }\ {\mathbb {R}}^3,\\ (-\Delta )^s \phi =u^2, &{} \text{ in }\ {\mathbb {R}}^3, \end{array}\right. } \end{aligned}$$

where \(s\in (\frac{3}{4},1)\) is a fixed constant, f is continuous, superlinear at infinity with subcritical or critical growth and V and f are asymptotically periodic in x. Applying the method of Nehari manifold and Lusternik–Schnirelmann category theory, three existence results are given.

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Acknowledgements

We would like to thank the anonymous referee for his/her careful readings of our manuscript and the useful comments. This work is supported by National Natural Science Foundation of China (No.11961081,12261107,12101546) and Yunnan Key Laboratory of Modern Analytical Mathematics and Applications (No. 202202AN210064).

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  1. Department of Mathematics, Yunnan Normal University, Kunming, 650500, China

    Guangze Gu, Changyang Mu & Zhipeng Yang

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  1. Guangze Gu
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GG and CM wrote the main results text, ZY wrote the main introduction text. All authors reviewed the manuscript.

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Correspondence to Zhipeng Yang.

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Gu, G., Mu, C. & Yang, Z. Existence and Multiplicity of Solutions for a Fractional Schrödinger–Poisson System with Subcritical or Critical Growth. Qual. Theory Dyn. Syst. 22, 63 (2023). https://doi.org/10.1007/s12346-023-00756-5

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