报告题目:Some recent results related to the prescribed fractional Q-curvatures problems

报告人:唐仲伟教授（北京师范大学数学科学学院）

报告时间:2025年12月7日8:30-10:30

报告地点:数学与统计学院145会议室

报告摘要:In this talk, I present some results about the compactness, existence and multiplicity of the solutions to the prescribing fractional $Q$-curvature problem. At first, we consider the fractional order is $2\sigma$ on $n$-dimensional standard sphere when $n − 2\sigma = 2$, $\sigma = 1 + m/2$, $m\in \mathbb{N}_+$, we obtain some compactness and existness results. Secondly, by combining critical points at infinity approach with Morse theory we obtain existence results under suitable pinching conditions. Thirdly, we obtain some results on the density and multiplicity of positive solutions to the prescribed fractional $Q$-curvatures problems for $\sigma\in(0,1)$ and $\sigma\in(1,\frac{n}{2})$ is an integer. This is a joint work with Dr. Yan Li, Heming Wang and Ning Zhou.

报告人简介:唐仲伟：北京师范大学数学科学学院教授、博士生导师，现任该院党委书记，兼任北京数学会副会长，2004年获中国科学院数学与系统科学研究院博士学位后进入北京师范大学任教，历任讲师、副教授，2016年晋升教授。2007年至2009年作为洪堡学者赴德国吉森大学访问研究。研究方向为偏微分方程与非线性分析，聚焦非线性薛定谔方程及方程组、分式Q-曲率问题。参与复合材料中的偏微分方程等课题，合著《偏微分方程》专著，在Int. Math. Res. Not.、J. Funct. Anal.、Calc. Var. Partial Differential Equations、J. Differential Equation、Nonlinearity、Pacific J. Math.、Sci. China Math.等期刊发表论文70余篇。