Stability And Lyapunov Inequalities For Some Hamiltonian Systems

In this paper,we discuss the Lagrange stability of impulsive Duffing equations via Moser's twist theorem and the Lyapunov inequalities for linear Hamiltonian systems undergoing suitable impulses.The main work of this paper is divided into four chapters.Chapter 1 is the introduction.We briefly introduce the impulsive differential equations and its application,the background and history of Duffing equations and linear Hamiltonian systems,and the main work and structure of this paper.In chapter 2,we discuss the Lagrange stability for Duffing equations with suitable impulses.By Moser's twist theorem,we prove that all solutions are bounded for all time and that there are many(positive Lebesgue measure)quasiperiodic solutions clustering at infinity.In chapter 3,by using the matrix measure method and impulsive equivalent transformation,we establish several Lyapunov inequalities for linear Hamiltonian systems undergoing suitable impulses.These results extend some well-known results on linear Hamiltonian systems to linear impulsive Hamiltonian systems.In chapter 4,we summarize the main results of the whole paper and look forward to the further research work.