报告题目：Ground state solutions of discrete nonlinear Schrödinger equations with bounded potentials
报 告 人：周展教授广州大学
报告时间：2020年10月28日星期三下午19:30-21:30
报告地点：腾讯会议ID：355415420
报告摘要：In this talk, we will consider the existence of ground state solutions for a class of discrete nonlinear Schrödinger equations with a sign-changing potential V that converges at infinity and a nonlinear term being asymptotically linear at infinity. The resulting problem engages two major difficulties: one is that the associated functional is strongly indefinite and the other is that, due to the convergency of the potential V at infinity, the classical methods such as periodic translation technique and compact inclusion method cannot be employed directly to deal with the lack of compactness of the Cerami sequence. New techniques are developed in this work to overcome these two major difficulties. This enables us to establish the existence of a ground state solution and derive a necessary and sufficient condition for a special case. To the best of our knowledge, this is the first attempt in the literature on the existence of a ground state solution for the strongly indefinite problem under no periodicity condition on the bounded potential and the nonlinear term being asymptotically linear at infinity. This is a joint work with Prof. Jianshe Yu and Dr. Genghong Lin.
报告人简介：周展，二级教授、博士生导师，教育部“长江学者和创新团队发展计划”创新团队带头人，享受国务院政府特殊津贴专家，广州市“优秀专家”，中国数学会理事。现任广州大学应用数学研究中心执行主任，数学与信息科学学院副院长。1985年7月毕业于湘潭大学数学系获学士学位，1988年7月毕业于湖南大学应用数学专业获硕士学位并留校任教，1998年6月获湖南大学应用数学专业博士学位。1999年6月破格晋升为教授，2003年12月被遴选为博士生导师。受国家留学基金委资助，2000年9月前往加拿大访问一年。先后应邀访问香港城市大学、应邀访问加拿大罗瑞尔大学、西安大略大学、新布伦瑞克大学。主持长江学者和创新团队发展计划2项、国家自然科学基金6项、高等学校博士点基金2项及教育部优秀青年教师资助计划等科研项目多项。作为负责人，获广州市首批建设科研创新学术团队。近年来在《J. Differential Equations》、《Nonlinearity》、《Proc.Royal Soc. Edinburgh》和《中国科学》(英文版)等重要刊物发表高水平科研论文80多篇，先后获得湖南省科技进步一等奖、湖南省自然科学优秀论文一等奖、第五届“秦元勋数学奖”、广东省高等学校“千百十人才培养工程”第六批先进个人。