Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (6): 1682-1704.

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Multiplicity of Solutions to Fractional Critical Choquard Equation

Lin Chen(),Fanqin Liu*()   

  1. School of Mathematics and Statistics, Jiangxi Normal University, Nanchang 330022
  • Received:2021-12-03 Online:2022-12-26 Published:2022-12-16
  • Contact: Fanqin Liu;


In this paper, we are concerned with the multiplicity of solutions for the following fractional Laplacian problemwhere $\Omega\subset\mathbb{R} ^N$ is an open bounded set with continuous boundary, $N>2s$ with $s\in(0, 1)$, $\lambda$ is a real parameter, $\mu\in(0, N)$ and $q\in[2, 2^\ast_s)$, where $^\ast_{s}=\frac{2N}{N-2s}$, $^\ast_{\mu, s}=\frac{2N-\mu}{N-2s}$. Using Lusternik-Schnirelman theory, there exists $\bar{\lambda}>0$ such that for any $\lambda\in(0, \bar{\lambda})$, the problem has at least $cat_\Omega(\Omega)$ nontrivial solutions provided that $q=2$ and $N\geq4s$ or $q\in(2, 2^\ast_s)$ and $N>\frac{2s(q+2)}{q}$.

Key words: Choquard equation, Critical exponent, Lusternik-Schnirelman theory

CLC Number: 

  • O175.2