The Multiple Existence Of Odd Periodic Solutions For A Kind Of Second-order Hamiltonian System Resonance Problem

Due to the close relation with definite solution of the problem in the physics,chemistry,biology,engineering and other fields,the existence and multiplicity of solution of differential equations have become an important topic in the field of differential equations and applications.In this thesis,by using Z2 type index Theorem,some new results about the existence and multiplicity of solution for a class of second Hamiltonian systems which improve or extend some results literatures.This thesis is divided into two chapters;its main contents are as follows.The first chapter introduces the background knowledge and research overview of the research questions,and at the end of the chapter gives some basic theories.The seconcd chapter mainly introduces the existence anf multiplicity of periodic solutions of second-order Hamiltonian systems.This chapter discusses the existence and multiplicity results of odd periodic solutions for a class of subquadratic second Hamiltonian systems.In the first section,some preliminaries are given and variational frameworks established.In the second and third section,byZ2-type index theory,we study the solution of systems under two cases of a parameter ranged between two adjacent eigenvalues and the resonance,and obtain finite pairs of nontrivial periodic solutions.