Lecturer:QIAN Dingbian

Abstract:

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.

Introduction to the Lecturer:

QIAN Dingbian, Professor of Soochow University, received a doctorate from Peking University in 1992. He has long been engaged in research related to the ordinary differential equations and dynamical systems, presiding over 6 research projects of the National Natural Science Foundation of China and publishing numerous high-quality papers in terms of invariant tori, stability and periodic solution concerning the Hamiltonian system. With regard to teaching, he was awarded the First Prize of Jiangsu Teaching Achievement Award. In addition, as the main member of the national-level excellent courses (mathematical analysis and exercises course) and teaching team (basic mathematics course teaching) of Soochow University, he and a team of professional teachers headed by Professor XIE Huimin jointly compiled two volumes ofLecture Notes on Mathematical Analysis Exercises Course, which were selected as Jiangsu Excellent Teaching Materials.

Invitee:

SI Jianguo, Professor from Mathematics School

Time:

10:00-11:00, March 15 (Tuesday)

Venue:

Tencent Rooms ID: 728-343-795

Sponsor: Mathematics School of Shandong University