报告题目：Concentrated solutions to nonlinear Schrödinger equations with very degenerate potentials

报 告 人：彭双阶，华中师范大学教授，博导，副校长

报告摘要：This talk is related to a singularly perturbed nonlinear Schrodinger equation. We obtain a more accurate location for the concentrated points,the existence and the local uniqueness for positive peak solutions when the potential V(x) 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 lower dimensional ellipsoid, or a part of hyperboloid of one sheet or two sheets, we obtain the number and symmetry of k-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 V(x).

报告人简介：彭双阶，华中师范大学博导，教授，副校长。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、教育部科学技术重点项目等。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 Rational Mech. Anal.,  Indana Unv.Math J.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。

邀请人：非线性泛函分析与微分方程科研团队

报告时间：2021年10月15日（周五）下午15:30-16:30

报告地点：长清湖校区文渊楼B区119室

主办单位：伟德国际1946源自英国