题目: Some existence and compactness results related to prescribed fractional Q-curvatures problems

报告专家：唐仲伟教授，北京师范大学数学科学学院

时间：2024年5月26日（周日）10：00 - 11：00

地点：9-122会议室

报告摘要: In this talk, I present some results about the compactness and existence results of the solutions to the prescribing fractional Q-curvature problem. At first, we consider the fractional order is on -dimensional standard sphere when , , . The compactness results are novel and optimal. In addition, we proved a degree-counting formula of all solutions to achieve the existence. From our results, we can know where blow up occur. Furthermore, the sequence of solutions that blow up precisely at any finite distinct location can be constructed. It is worth noting that our results include the case of multiple harmonic. Secondly, by combining critical points at infinity approach with Morse theory we obtain new existence results under suitable pinching conditions. This is a joint work with Dr. Yan Li，Heming Wang and Ning Zhou.

专家简介：唐仲伟，教授，博士生导师，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。2004年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， 2007年9月-2009年9月受德国洪堡基金会资助在德国吉森大学做洪堡学者，自2004年8月起在北京师范大学数学科学学院工作。主要研究领域为偏微分方程及非线性分析，在偏微分方程(组)的多峰解问题、薛定谔方程的基态解刻画等方面做出了一系列重要的研究工作，在 IMRN、CVPDE、Nonlinearity、JDE等期刊上发表SCI论文60余篇，主持国家自然科学基金6项。

作者：郭伦；编辑：刘鹍；审核：郭晖；上传：郭敏。