数学科学学院学术报告

--- 分析、偏微分方程与动力系统讨论班 (2025春季第8讲)

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

唐仲伟 (北京师范大学)

时间：5月19日（周一）下午16:30-17:30

地点：沙河校区国实E803

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，北京师范大学教授，博士生导师，现担任北京师范大学数学科学学院党委书记、教学指导委员会主任。1994.9-2001.7先后在西北师范大学数学系（现数学与统计学院）获得学士和硕士学位，2004年7月在中国科学院数学与系统科学研究院应用数学所获得博士学位后到北京师范大学工作至今，2007.9-2009.9受德国洪堡基金会资助在德国吉森大学做洪堡学者。主要研究领域为偏微分方程及非线性分析，在IMRN, JFA, Nonlinearity, Calc. Var. Partial Differential Equations, J. Differential Equations，Pacific J. Math. 等期刊上发表SCI论文70余篇，主持国家自然科学基金项目7项。

欢迎大家参加！

邀请人：戴蔚、彭发