报告承办单位: 数学与统计学院

报告题目: Non-trivial homoclinic solutions and ground state solutions for some discrete systems

报告摘要: In this talk, I will introduce some existence results of homoclinic solutions and ground state solutions for some discrete systems. In previous studies, potential functions are often assumed to be coercive, which is merely a special case of being strongly indefinite. We address this gap and build upon prior research in this direction. The arising difficulty is that the energy functional is unbounded from both above and below, which is induced by the strongly indefinite potential $V$. To tackle this challenge, we develop a strongly indefinite version of the compact embedding theorem. It is shown that the boundedness of the Cerami sequence and linking structure of the energy functional remain even in this case. To the best of our knowledge, this is the first attempt to investigate a discrete system involving a strongly indefinite potential. Our results also improve upon some existing results in the literature. This is a joint work with Yanshan Chen and Bengxing Zhou.

报告人姓名: 周展

报告人所在单位: 广州大学

报告人职称: 教授

报告时间: 2026年7月3日（星期五）上午10:00

报告地点: 理科楼A212

邀请人：胡海军

报告人简介: 周展，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，享受国务院政府特殊津贴专家。1985年获湘潭大学数学系学士学位，1988年、1998年先后在湖南大学获应用数学硕士、博士学位。1988年起历任湖南大学助教、讲师、副教授、教授。2000年任加拿大约克大学访问学者，2011年7月应邀访问香港城市大学。主持国家自然科学基金7项、教育部项目2项，在《J. Differential Equations》《Physica D》等期刊发表论文100余篇，获湖南省科技进步一等奖、广东省自然科学一等奖及第五届秦元勋数学奖 。主要研究方向为泛函微分方程和差分方程，涉及离散非线性薛定谔方程、φ-Laplacian差分方程等领域。