Periodic solutions with prescribed minimal period for second order even Hamiltonian systems

讲座时间 Datetime: 2022年11月13日，星期天，9:00-10:30

地点 Venue: 腾讯线上会议：262-919-349

主持人 Host：唐德 副教授

报告人 Speaker: 郭志明 教授

单位 Affiliation: 广州大学

报告摘要 Abstract:

In this paper, we develop a new method to study Rabinowitz's conjecture on the existence of periodic solutions with prescribed minimal period for second order even Hamiltonian system without any convexity assumptions. Specifically, we first study the associated homogenous Dirichlet boundary value problems for the discretization of the Hamiltonian system with given step length and obtain a sequence of nonnegative solutions corresponding to different step lengths by using discrete variational methods. Then, using the sequence of nonnegative solutions, we construct a sequence of continuous functions which can be shown to be precompact. Finally, by utilizing the limit function of convergent subsequence and the symmetry of the potential, we will obtain the desired periodic solution. In particular, we prove Rabinowitz's conjecture in the case when the potential satisfies a certain symmetric assumption.

报告人简介：广州大学数学与信息科学学院二级教授、博士生导师。2001年博士毕业于中山大学，2009 年在加拿大西安大略大学访问一年。多年来一直从事离散系统、泛函微分方程及生物数学模型的理论与应用研究，在《Journal of Differential Equations》、《Journal of London Mathematical Society》、《Journal of Dynamics and Differential Equations》、《Journal of Mathematical Biology》、 《中国科学》等国际国内重要刊物上发表论文70多篇，其中SCI收录50多篇。先后主持国家自然科学基金面上项目4项、参加国家自然科学基金重点项目1项，获得广东省自然科学奖一等奖1。