带Hardy项和一般非线性项分数阶椭圆方程的移动平面法  

The Method of Moving Planes for Fractional Order Elliptic Equations with Hardy and General Nonlinear Terms

作　　者：张晓亚 

机构地区：[1]浙江师范大学数学科学学院,浙江 金华

出　　处：《应用数学进展》2023年第9期3804-3813,共10页Advances in Applied Mathematics

摘　　要：本文应用直接移动平面法,研究带Hardy项的分数阶拉普拉斯方程的正解的对称性和单调性。首先,关于某一点作Kelvin变换,然后建立了狭窄区域上的极值原理和无穷远处衰减原理,利用这一原理和移动平面法得到正解关于某一点对称并且关于这一点先增后减的结果。In this paper, we study the symmetry and monotonicity of positive solutions for fractional Laplace equations involving the Hardy potential. Firstly, the Kelvin transform is performed on a certain point, and then we establish a narrow region principle and decay at infinity principle. By using this principle and the moving plane method, the result that the positive solution is symmetric about a certain point and first increases and then decreases is obtained.

关 键 词：Hardy项 分数阶拉普拉斯方程 移动平面法 

分 类 号：O17[理学—数学]