Almost Periodic Solutions Of Nonlinear Duffing Equations With Damping

Duffing equation is one of the commonest examples to describe the resonance, harmonic vibration, subharmonic vibration,quasi-periodic vibration, almost periodic vibration, singular attractors and chaos phenomena, etc. And it has abroad applications in mechanics and electronic technologies.This thesis, which is divided into three parts, is concerned with the existence and uniqueness of the almost periodic solutions of nonlinear Duffing equations with damping.In the preface, the author simply introduces the history and development of Duffing equations, and then naturally brings up the problems investigated on.In the chapter 1, the author studies the existence and uniqueness of nonlinear Duffing equations with damping,which has ordinary coefficient. The results of Berger and Chen are extended. And the variational method is proved to be available to solve the existence and uniqueness of the almost periodic solutions of nonlinear Duffing equations with damping.The chapter 2 investigates the existence and uniqueness of the almost periodic solutions of nonlinear Duffing equations with damping,which has variable coefficient .The corresponding variational structure of Duffing equation is presented,and the results in the first chapter are extended and have more applications.The chapter 3 is concerned with a special Duffing type of nonlinear systems with damping. The relative results are acquired from scalar equations to high-order systems.