3 papers
math.AP2024
The direct moving sphere for fractional Laplace equation
Congming Li, Meiqing Xu, Hui Yang +1
This paper works on the direct method of moving spheres and establishes a Liouville-type theorem for the fractional elliptic equation \[ (-Δ)^{α/2} u =f(u) ~~~~~~ \text{in } \mathb…
math.AP2023
Direct Method of Scaling Spheres for the Laplacian and Fractional Laplacian Equations with Hardy-Henon Type Nonlinearity
Meiqing Xu
In this paper, we focus on the partial differential equation \begin{equation*} (-Δ)^\fracα{2} u(x)=f(x,u(x))\;\;\;\;\text{ in }\mathbb{R}^n, \end{equation*} where . By t…
math.AP2023
A priori estimates for higher-order fractional Laplace equations
Yugao Ouyang, Meiqing Xu, Ran Zhuo
In this paper, we establish a priori estimates for the positive solutions to a higher-order fractional Laplace equation on a bounded domain by a blowing-up and rescaling argument.…