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math.AP2026
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…
math.AP2026
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…
math.AP2025
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…