Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (3): 702-722.

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Existence and Multiplicity of Solutions for a Fractional Choquard Equation with Critical or Supercritical Growth

Xianyong Yang1,2(),Xianhua Tang2,*(),Guangze Gu3()   

  1. 1 School of Preparatory Education, Yunnan Minzu University, Kunming 650500
    2 School of Mathematics and Statistics, Central South University, Changsha 410205
    3 School of Mathematics, Yunnan Normal University, Kunming 650500
  • Received:2020-03-31 Online:2021-06-01 Published:2021-06-09
  • Contact: Xianhua Tang;;
  • Supported by:
    the NSFC(11971485);the NSFC(11661083);the NSFC(11861078);the NSFC(11771385);the NSFC(11901345);the Hunan Provincial Innovation Foundation for Postgraduate and the Fundamental Research Funds for the Central Universities of Central South University


We consider the following fractional Choquard equation with critical or supercritical growth where $s \in (0, 1)$, $\mu\in (0, N)$, $N>2s$, $q\geq 2_{\mu, s}^\ast$, $f$ is a continuous function. It is well-known that $2_{\mu, s}^\ast=\frac{2N-\mu}{N-2s}$ and $2_{\mu, s}=\frac{2N-\mu}{N}$ are critical exponents for the above equation in the sense of Hardy-Littlewood-Sobolev inequality. Many existence results have been established for $q \in[2_{\mu, s}, 2_{\mu, s}^\ast]$ in recent years. Here we are interested in critical or supercritical case for the above equation. Under some assumptions of $f$, the existence and multiplicity of solutions for the above equation can be obtained by applying some analytical techniques.

Key words: Fractional Choquard equation, Critical, Supercritical growth, Truncation technique

CLC Number: 

  • O175.2