报告题目：Topic I: Pohozaev type identities and their applications；Topic II: Concentrated solutions to nonlinear Schrodinger equations with very degenerate potentials

报告人：彭双阶

报告时间：2023年08月19日（周六）15:00-18:30

报告地点：数学楼315会议室

报告摘要：Part I: In this talk, we first introduce the Pohozaev identities, and then apply them to study the singularly perturbed problems and elliptic problems for the uniqueness results and the existence of infinitely many solutions.

Part II: We talk about a type of singularly perturbed nonlinear Schrodinger equation with a potential and obtain a more accurate location for the concentrated points, the existence and the local uniqueness for positive multi-peak solutions when the potential possesses non-isolated critical points by using the modified finite dimensional reduction method based on local Pohozaev identities. Moreover, for several special potentials, with its critical point set being a low-dimensional ellipsoid, or a part of hyperboloid of one sheet or two sheets, we obtain the number and symmetry of multi-peak solutions by using local uniqueness of concentrated solutions. Here the main difficulty comes from the different degenerate rate along different directions at the critical points of the potential. This is a joint work with Peng Luo, Kefan Pan and Yang Zhou.

报告人简介：彭双阶，教授、华中师范大学党委常委、副校长、博士生导师。2011年获得国家杰出青年科学基金，2012年入选首批“湖北省高端人才引领培养计划”。曾获得教育部自然科学二等奖和湖北省自然科学奖特（一）等奖，国家级教学成果奖二等奖。先后主持了国家自然科学基金重点项目、教育部“长江学者与创新团队”发展计划项目等。共发表学术论文100余篇，其中多篇论文发表在Adv.Math.、J.Math.Pures.Appl.、Proc. London Math.Soc.、Tran. Amer. Math. Soc.、Math.Ann、 Arch. Ratinal. Mech.Anal.、 Ann.I.H.Poincaré- AN等重要学术期刊上，其研究成果引起了国内外专家的广泛关注，被美国、德国、意大利、澳大利亚等国家的数学家大量引用或推广，并用来解决其它的问题。