分数阶Kirchhoff型约束变分问题Schwarz对称极小解的存在性  

Existence of Schwarz Symmetric Minimizers for Fractional Kirchhoff Constrained Variational Problem

作　　者：魏均平 黄小梦 张贻民 Wei Junping;Huang Xiaomeng;Zhang Yimin(Center for Mathematical Sciences,Wuhan University of Technology,Wuhan 430070)

机构地区：[1]武汉理工大学数学科学研究中心,武汉430070

出　　处：《数学物理学报（A辑）》2022年第6期1719-1728,共10页Acta Mathematica Scientia

基　　金：国家自然科学基金(12171379)。

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)(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)(R^(N))上极小解的存在性与非线性项的指数和约束∫_(RN)|u|^(2)dx=c^(2)中参数c的关系.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)(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∫_(RN)|u|^(2)dx=c^(2)was discussed.

关 键 词：约束变分 极小解 分数阶Kirchhoff问题 Schwarz对称 

分 类 号：O175.25[理学—数学]