7 papers
The direct moving plane method for weak solutions of the fractional -Laplacian
Meiqing Xu, Hui Yang
In this paper, we develop the method of moving planes entirely in the weak formulation for the fractional -Laplacian in the singular range . We first establish a small…
On the structure of isolated singularities for semilinear elliptic equations
Meiqing Xu, Hui Yang
In this paper, we study isolated singularities of the following semilinear elliptic equation in , where $n\ge 3…
Liouville theorems for conformal -curvature equations
Meiqing Xu, Hui Yang
In this paper, we study the non-existence of positive solutions for the following conformal -curvature equation \begin{equation*} (-Δ)^σu = K(x) u^{\frac{n+2σ}{n-2σ}} \quad \tex…
Gaussian limit for Pfaffian point processes
Kai Wang, Mei Xu
We prove a central limit theorem for linear statistics of a broad class of Pfaffian point processes. As an application, we derive Gaussian limits for scaled linear statistics of st…
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…
Maximum principles for nonlinear integro-differential equations and symmetry of solutions
Huxiao Luo, Meiqing Xu
In this paper, we study the semilinear integro-differential equations \begin{equation*} \mathcal{L}_{K}u(x)\equiv C_n\text{P.V.}\int_{\R^n}\left(u(x)-u(y)\right)K(x-y)dy=f(x,u), \e…
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…