一、题目

An extension of the Poincare-Birkhoff theorem for Hamiltonian systems coupling resonant linear components with twisting components

二、主讲人

钱定边

三、摘要

In our talk we improve a generalized saddle point theorem by J. Liu using Lusternik-Schnirelmann variational methods. Based on this new saddle point theorem we prove an extension of the Poincare-Birkhoff theorem for Hamiltonian systems coupling resonant linear components with twisting components. As an application of this version of the Poincare--Birkhoff theorem, we obtain the multiplicity result of subharmonic solutions for a mixed type weakly-coupled Hamiltonian systems coupling superliner-sublinear components with Ahmad-Lazer-Paul type resonance components. Our abstract theorems could be used not only for the researches for periodic dynamics of Hamiltonian systems, but also for the researches for other models of nonlinear analysis.

四、主讲人简介

钱定边，苏州大学教授，1992年获北京大学博士学位。长期从事常微分方程与动力系统研究，主持过6项国家自然科学基金研究项目，并在哈密顿系统的不变环面、稳定性，周期解研究方面发表过多篇高质量论文。教学上获得过江苏省教学成果奖一等奖，是苏州大学国家级精品课程（数学分析及习题课）和国家级教学团队（数学基础课教学）的主要成员，与谢惠民教授等一起编写的《数学分析习题课讲义》（上、下册）是江苏省精品教材。

五、邀请人

司建国 数学学院教授

六：时间

3月15日（周二）10:00-11:00

七、地点

腾讯会议ID：728-343-795

八、主办方

山东大学数学学院