6 papers · 1 filter
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…
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…