題目: Some existence and compactness results related to prescribed fractional Q-curvatures problems
報(bào)告專(zhuān)家：唐仲偉教授，北京師范大學(xué)數(shù)學(xué)科學(xué)學(xué)院
時(shí)間：2024年5月26日（周日）10：00 - 11：00
地點(diǎn)：9-122會(huì)議室
報(bào)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(zhuān)家簡(jiǎn)介：唐仲偉，教授，博士生導(dǎo)師，北京師范大學(xué)數(shù)學(xué)科學(xué)學(xué)院黨委書(shū)記、教學(xué)指導(dǎo)委員會(huì)主任。2004年在中國(guó)科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院應(yīng)用數(shù)學(xué)所獲得博士學(xué)位， 2007年9月-2009年9月受德國(guó)洪堡基金會(huì)資助在德國(guó)吉森大學(xué)做洪堡學(xué)者，自2004年8月起在北京師范大學(xué)數(shù)學(xué)科學(xué)學(xué)院工作。主要研究領(lǐng)域?yàn)槠⒎址匠碳胺蔷€(xiàn)性分析，在偏微分方程(組)的多峰解問(wèn)題、薛定諤方程的基態(tài)解刻畫(huà)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(fā)表SCI論文60余篇，主持國(guó)家自然科學(xué)基金6項(xiàng)。
作者：郭倫；編輯：劉鹍；審核：郭暉；上傳：郭敏。
