学术空间

Some recent results related to the prescribed fractional Q-curvatures problems

【数学与统计及交叉学科前沿论坛------高端学术讲座第150场】


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

报告时间:2025年4月17日周四16:00--17:00

报告地点:阜成路校区教二楼303


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,中国科学院数学与系统科学研究院应用数学所博士。北京师范大学教授、博士生导师,数学科学学院党委书记、教学指导委员会主任,北京市数学会副理事长。曾受德国洪堡基金会资助在德国吉森大学做洪堡学者(2007.9-2009.9)。主要从事偏微分方程及非线性分析等研究。在IMRN, JFA, Nonlinearity, Calc. Var. Partial Differential Equations, J. Differential Equations,Pacific J. Math. 等SCI收录期刊发表学术论文70余篇;主持完成多项国家自然科学基金项目。