Study On Periodic Solutions Of A Class Of Second Order Hamiltonian Systems And Impact Hamiltonian Systems

This paper considers the multiplicity of periodic solutions about a class of sec-ond order nonautonomous Hamiltonian systems and second order impact Hamiltonian systems.For the first class,it considers periodic solutions for a class of second order nonautonomous Hamiltonian systems.On the basis of the existence results in paper^[1],two multiplicity results of periodic solutions of Hamiltonian systems by adding ap-propriate conditions and using minimax principle are proved.This paper weaken the assumptions compared to the multiplicity results previously presented in paper^[2,3](see chapter 2).For the second class,it mainly studies on impact Hamiltonian systems with obstacles.Under the new hypothesis conditions and the new collision axis,the results that have appeared in paper^[4]by using the generalized nonsmooth saddle point theorem are generalized(see chapter 3).This paper is divided into three parts.In the first chapter,we introduce the re-search background,research history and research methods of Hamiltonian systems,we also introduce the research methods,research results and innovation of this paper.In the second chapter,we introduce the research background,research methods and relat-ed basic knowledge of a class of second order Hamiltonian systems,and give the proof of the multiplicity of periodic solutions of the Hamiltonian systems as well as an ex-ample.This result has been accepted for publication by Acta Scientiarum Naturalium Universitatis Nankaiensis.In the third chapter,we introduce the research background,research methods and related basic knowledge of impact Hamiltonian systems,and give the proof of the multiplicity of periodic solutions of the impact system as well as an ex-ample.This result has been published in the mathematics SCI journal Boundary Value Problems.