4 papers
A positive answer to the generalized Chang-Yang conjecture on
Changfeng Gui, Tuoxin Li, Juncheng Wei +1
We prove that for every integer and , Beckner's inequality \[ \fracα{2}\int_{\mathbb{S}^N}u(P_{N}u) dw+(N-1)!\int_{\mathbb{S}^N}u dw-\frac{(N-1)!}{N}\l…
Sharp Beckner's Inequalities for Axially Symmetric Functions on
Changfeng Gui, Tuoxin Li, Juncheng Wei +1
We prove that for every integer and , Beckner's inequality \begin{equation*} \fracα{2}\int_{\mathbb{S}^N}u(P_{N}u) dw+(N-1)!\int_{\mathbb{S}^N}u dw-\fr…
On the Classification of blow-up solutions of a singular Liouville equation on the disk
Zhijie Chen, Houwang Li, Tuoxin Li +1
We study the blow-up behavior of solutions to the singular Liouville equation \[ Î\tilde u+λe^{\tilde u}=4Ïαδ_0 \quad\text{in }B,\quad \tilde u=0 \quad\text{on }\partial B, \]…
Infinitely many solutions for the prescribed scalar curvature problem with volcano-like curvature
Tuoxin Li, Juncheng Wei, Haidong Yang
In this paper, we consider the following prescribed scalar curvature problem: \begin{equation*} -Îu = K(x) u^{\frac{n+2}{n-2}}, \quad u>0\quad\hbox{in}\quad \mathbb{R}^n, \quad u…