2 citations · 3 across the 3 of their papers we have counts for
4 papers · 1 filter
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…
A Liouville theorem for -harmonic functions in
Wenxiong Chen, Congming Li, Lizhi Zhang +1
In this paper, we consider -harmonic functions in the half space : \begin{equation} \left\{\begin{array}{ll} (-Δ)^{α/2} u(x)=0,~u(x)>0, & x\in\mathbb{R}^n_+, \\…
A Liouville theorem for high order degenerate elliptic equations
Genggeng Huang, Congming Li
In this paper, we apply the moving plane method to the following high order degenerate elliptic equation,\begin{equation*} (-A)^p u=u^α\text{ in } \mathbb R^{n+1}_+,n\geq 1, \end{e…
Shooting Method with Sign-Changing Nonlinearity
Ze Cheng, Congming Li
In this paper, we study the existence of solution to a nonlinear system: \begin{align} \left\{\begin{array}{cl} -Δu_{i} = f_{i}(u) & \text{in } \mathbb{R}^n, u_{i} > 0 & \text{in }…