分数阶Kirchhoff型约束变分问题Schwarz对称极小解的存在性

数学物理学报 ›› 2022, Vol. 42 ›› Issue (6): 1719-1728.

分数阶Kirchhoff型约束变分问题Schwarz对称极小解的存在性

魏均平(),黄小梦(),张贻民*()

^{武汉理工大学数学科学研究中心, 武汉 430070}

收稿日期:2022-01-07 出版日期:2022-12-26 发布日期:2022-12-16
通讯作者: 张贻民 E-mail:weijunpingacca@163.com;hhuangxiaomeng@126.com;zhangym802@126.com
作者简介:魏均平, E-mail: weijunpingacca@163.com|黄小梦, E-mail: hhuangxiaomeng@126.com
基金资助:
国家自然科学基金(12171379)

Existence of Schwarz Symmetric Minimizers for Fractional Kirchhoff Constrained Variational Problem

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

^{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)

摘要/Abstract

摘要：

该文主要讨论一般非线性项情形下一类分数阶Kirchhoff型约束变分问题在空间 $H^s(\mathbb{R}^N)$ 上极小解的存在性和Schwarz对称性.利用单调递减重排不等式和伸缩技巧, 当非线性项满足合适的条件时, 该文细致的讨论了相应约束变分问题在空间 $H^s(\mathbb{R}^N)$ 上极小解的存在性与非线性项的指数和约束 $\int_{\mathbb{R}^N}|u|^2{\rm d}x=c^2$ 中参数 $c$ 的关系.

关键词: 约束变分, 极小解, 分数阶Kirchhoff问题, Schwarz对称

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

中图分类号:

O175.25

魏均平,黄小梦,张贻民. 分数阶Kirchhoff型约束变分问题Schwarz对称极小解的存在性[J]. 数学物理学报, 2022, 42(6): 1719-1728.

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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