The Existence Of Periodic Solutions For Second Order Hamiltonian Systems With Damped Vibration

In this paper, by using variational method, we deal with the existence of periodic solutions for two classes of second order Hamiltonian systems with damped vibration. Some new existence theorems are obtained via critical point theory under subquadratic condition, superquadratic condition and local asymptotically quadratic condition, respectively. The paper divided into five chapters. The main contents are as follows:In the first chapter, we sketch the present situation for our investigating problems and the main work of this paper.In the second chapter, we introduce some preliminaries which will be used in this paper.In the third chapter, by using the saddle point theorem, we concern with the existence of periodic solutions for the following second order damped vibration systems On the one hand, we extend the results to the damped vibration systems. On the other hand, we introduce a new control function and obtain some new existence theorems, which generalize and improve some recent results in the literature.In the fourth chapter, by using the generalized mountain pass theorem, we study the existence of periodic solutions for the following second order damped vibration systems A new class of superquadratic condition are introduced and some meaningful conclusions are obtained under this condition.In the fifth chapter, by using the saddle point theorem, we continue studying the existence of periodic solutions for the following second order damped vibration systems Some new solvability conditions are presented under local asymptotically quadratic condition, and some new results are obtained for Hamiltonian systems under the local condition.