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Fractional Schrödinger–Poisson system with critical growth and potentials vanishing at infinity

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  • Xinrui Zhang
  • Xiaoming He

Abstract

In this paper, we are concerned with the existence of positive solutions for a class of fractional Schrödinger–Poisson system with critical nonlinearity and multiple competing potentials, which may decay and vanish at infinity. Under some local conditions, we show the existence and concentration of positive solutions by using the modified penalization method and concentration–compactness principle.

Suggested Citation

  • Xinrui Zhang & Xiaoming He, 2023. "Fractional Schrödinger–Poisson system with critical growth and potentials vanishing at infinity," Mathematische Nachrichten, Wiley Blackwell, vol. 296(5), pages 2167-2191, May.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:5:p:2167-2191
    DOI: 10.1002/mana.202100094
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    1. Zhipeng Yang & Yuanyang Yu & Fukun Zhao, 2019. "The concentration behavior of ground state solutions for a critical fractional Schrödinger–Poisson system," Mathematische Nachrichten, Wiley Blackwell, vol. 292(8), pages 1837-1868, August.
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