Lagrange Stability And Related Problems Of Some Impulsive Equations

This thesis mainly studies Lagrange stability and related problems of some impulsive equations via KAM Theory.It is consisted of four chapters.Chapter 1 is the introduction,we introduce KAM theory and its applications,the background and history of Duffing equations and pendulum-type equations,the content of Moser's twist theorem,and the main work of this thesis.In Chapter 2,we study Lagrange stability and related problems for impulsive Duffing equations.By KAM theorem,we prove the existence of invariant tori of the impulsive Duffing equation undergoing suitable impulses,and we prove that all solutions of the impulsive Duffing equation are bounded for all time(Lagrange stable).In Chapter 3,we study Lagrange stability and related problems for impulsive pendulum-type equations.By KAM theorem,we prove the existence of invari-ant tori of the impulsive Duffing equation undergoing suitable impulses,and we prove that all solutions of the impulsive Duffing equation are bounded for all time(Lagrange stable).In Chapter 4,we summarize the full thesis and pointed out the further re-search work.