分数阶Kirchhoff型约束变分问题Schwarz对称极小解的存在性

Abstract

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

Junping Wei,Xiaomeng Huang,Yimin Zhang. Existence of Schwarz Symmetric Minimizers for Fractional Kirchhoff Constrained Variational Problem[J].Acta mathematica scientia,Series A, 2022, 42(6): 1719-1728.

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References 27

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Existence of Schwarz Symmetric Minimizers for Fractional Kirchhoff Constrained Variational Problem

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