Homoclinic Orbits And Periodic Solutions For Several Kinds Of Hamiltonian Systems On Time Scales With Impulsive Effects

In this paper,we consider the existence of homoclinic orbits and periodic solutions for a class of Hamiltonian systems on time scales with impulsive effect and a class of delay Hamiltonian systems on time scales with impulsive effect respectively by applying critical point theorems.By choosing appropriate work space,establishing corresponding variational setting for these two problems,we obtain existence and multiplicity of periodic solutions for these systems.Especially,we also show the existence of nontrivial homoclinic orbits for these two kinds of problems,which just right are the limit of 2kT-periodic solutions.This paper consists of four chapters and the arrangement is as follows.Firstly,we describe the research background of impulsive differential equations?the research status of periodic solution and homoclinic orbits for Hamiltonian system and the main content in this paper.Secondly,we introduce some relevant knowledge with respect to calculus on time scales and critical point theory such as saddle point theorem,minimum action principle and Mountain pass lemma and assumed condition.Once again,we discuss the existence of periodic solutions for a class of Hamiltonian systems on time scales with impulsive effects by using the saddle point theorem,the minimum action principle and the three critical point theorem,and obtain homoclinic orbits of this system by using Mountain pass lemma and Maximum minimum principle.Finally,We study the existence of homoclinic orbits and periodic solutions for delay Hamiltonian systems on time scales with impulsive effect.The influence of delay on the existence of periodic solution and homoclinic orbits is overcome.