Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (6): 1719-1728.

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Existence of Schwarz Symmetric Minimizers for Fractional Kirchhoff Constrained Variational Problem

Junping Wei(),Xiaomeng Huang(),Yimin Zhang*()   

  1. Center for Mathematical Sciences, Wuhan University of Technology, Wuhan 430070
  • Received:2022-01-07 Online:2022-12-26 Published:2022-12-16
  • Contact: Yimin Zhang E-mail:weijunpingacca@163.com;hhuangxiaomeng@126.com;zhangym802@126.com
  • Supported by:
    the NSFC(12171379)

Abstract:

In this paper, the existence and Schwarz symmetry of minimizers for a fractional Kirchhoff constrained variational problem with general nonlinear term were studied in space $H^s(\mathbb{R} ^N)$. Using symmetric decreasing rearrangement inequality and scaling technique, the relation between existence of minimizers for a fractional Kirchhoff constrained variational problem with the exponent of nonlinear term and parameter $c$ in $\int_{\mathbb{R} ^N}|u|^2{\rm d}x=c^2$ was discussed.

Key words: Constrained variational, Minimizer, Fractional Kirchhoff problem, Schwarz symmetric

CLC Number: 

  • O175.25
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