6 papers
On Dolbeault's conjecture
Juncheng Wei, Zetian Yan, Zikai Ye
We prove sharp improved Sobolev inequalities on , , for antipodally even functions and for axially symmetric functions whose critical density h…
Complete classification of solutions for spin-1 Bose-Einstein condensates in R
Xiao Luo, Cunxin Wei, Juncheng Wei +1
Spin-1 Bose-Einstein condensates provide a fundamental platform for exploring quantum magnetism and coherent spin dynamics. Their three Zeeman components are coupled by spin-exchan…
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…
Axially Symmetric Rigidity for a -Curvature-Type Equation on
Changfeng Gui, Tuoxin Li, Juncheng Wei +1
We prove that for every even integer or , every axially symmetric solution to the -curvature-type problem $$ αP_N u + (N-1)!(1-\frac{e^{Nu}}{\int_{\math…
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…
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*} -Δu = K(x) u^{\frac{n+2}{n-2}}, \quad u>0\quad\hbox{in}\quad \mathbb{R}^n, \quad u \…