題目: Some existence and compactness results related to prescribed fractional Q-curvatures problems
報告專家：唐仲偉教授，北京師范大學數學科學學院
時間：2024年5月26日（周日）10：00 - 11：00
地點：9-122會議室
報告摘要: 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.
專家簡介：唐仲偉，教授，博士生導師，北京師范大學數學科學學院黨委書記、教學指導委員會主任。2004年在中國科學院數學與系統科學研究院應用數學所獲得博士學位， 2007年9月-2009年9月受德國洪堡基金會資助在德國吉森大學做洪堡學者，自2004年8月起在北京師范大學數學科學學院工作。主要研究領域為偏微分方程及非線性分析，在偏微分方程(組)的多峰解問題、薛定諤方程的基態解刻畫等方面做出了一系列重要的研究工作，在 IMRN、CVPDE、Nonlinearity、JDE等期刊上發表SCI論文60余篇，主持國家自然科學基金6項。
作者：郭倫；編輯：劉鹍；審核：郭暉；上傳：郭敏。
