Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (6): 1622-1633.

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Existence and Asymptotic Behavior of Ground State for Fractional p-Laplacian Equations

Yaling Han1,*(),Jianlin Xiang2()   

  1. 1 School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073
    2 Department of Mathematics, Wuhan University of Technology, Wuhan 430070
  • Received:2020-05-26 Online:2020-12-26 Published:2020-12-29
  • Contact: Yaling Han;
  • Supported by:
    the NSFC(61503415)


In this paper, existence and asymptotic behavior of a fractional p-Laplacian equation with biharmonic potential and critical nonlinear was considered. First, variational method is used to obtain the existence and nonexistence of ground state under different parameter β. Then, the technique of energy estimates was used to get the asymptotic properties of ground state as parameter β tends to critical case.

Key words: Ground states, Fractional p-Laplacian equations, Energy estimates

CLC Number: 

  • O175.2