Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (2): 470-490.

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Existence, Multiplicity and Concentration of Positive Solutions for a Fractional Choquard Equation

Weiqiang Zhang*(),Peihao Zhao()   

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000
  • Received:2021-04-22 Online:2022-04-26 Published:2022-04-18
  • Contact: Weiqiang Zhang E-mail:zhangwq19@lzu.edu.cn;zhaoph@lzu.edu.cn
  • Supported by:
    the NSFC(11471147)

Abstract:

We are concerned with the existence, multiplicity and concentration of positive solutions for the following fractional Choquard equation with subcritical nonlinearity where ε>0 is a parameter, s(0,1), (Δ)s is the fractional Laplace operator, V:RNR is a positive potential having global minimum, 0<μ<min{4s,N}, and F is the primitive of fC1(R,R) which is subcritical growth. The main research methods of this article are variational method and the Ljusternik-Schnirelmann theory.

Key words: Fractional Choquard equation, Variational method, Ljusternik-Schnirelmann theory, Positive solution, Concentrating phenomenon.

CLC Number: 

  • O175.2
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