7 papers
Symmetry, monotonicity, and asymptotics of singular solutions to semilinear elliptic equations
Xusheng Du, Hui Yang
In this paper, we study singular positive solutions to the semilinear elliptic equation where is a bounded or u…
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…
On isolated singularities of the conformal Gaussian curvature equation and -curvature equation
Hui Yang, Ronghao Yang
In this paper, we study the isolated singularities of the conformal Gaussian curvature equation \[ -Δu = K(x) e^{u} \quad ~ in ~ B_{1} \setminus \{ 0 \}, \] where $B_1 \setminus \{…
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…
Asymptotic expansions for conformal scalar curvature equations near isolated singularities
Xusheng Du, Hui Yang
In this paper, we study asymptotic expansions of positive solutions of the conformal scalar curvature equation $$ - Δu = K(x) u^\frac{n + 2}{n - 2} ~~~~~~ \textmd{in} ~ B_1 \setmin…