Marked With The Pulse Order Non-autonomous Hamiltonian System Periodic Solution Of The Existence Of Problems,

This master thesis is concerned with the existence of periodic solutions for some non-autonomous second order Hamiltonian systems with impulses in the derivative and the existence of periodic solutions for second order differential equations on time scales by using critical point theory. This work is composed of four chapters.Chapter 1 introduces the background of this thesis and depicts the research prob-lems.Chapter 2 presents some preliminary results concerning critical point theory and calculus on time scales.Chapter 3 investigates the existence of periodic solutions for a class of non-autonomous second order Hamiltonian systems with impulses in the derivative by using the least action principle without the coerciveness assumption. Some related results are generalized and improved.Chapter 4 deals with the existence of periodic solutions for a class of second order dynamic differential equations on time scales by using the least action principle. Some new existence theorems are obtained without the coerciveness assumption.