具有跳跃项的Duffing方程的拟周期解  

Quasi-Periodic Solutions for Duffing Equation with Jumping Term

作　　者：张新丽 ZHANG Xin-Li(School of Mathematical Sciences,Ocean University of China,Qingdao 266100,China;School of Mathematics and Physics,Qingdao University of Science and Technology,Qingdao 266061,China)

机构地区：[1]中国海洋大学数学科学学院,山东青岛266100 [2]青岛科技大学数理学院,山东青岛266061

出　　处：《中国海洋大学学报（自然科学版）》2020年第4期145-150,共6页Periodical of Ocean University of China

基　　金：国家自然科学基金项目(11571327)资助。

摘　　要：本文研究了一类具有非对称项和有界扰动项的Duffing方程。当扰动项是拟周期函数时,利用典则变换和光滑拟周期扭转映射的不变曲线定理,证明了方程任意解的有界性和拟周期解的存在性。In this paper,we study a type of Duffing equation which has asymmetric term and jumping nonlinearity.When the perturbation term is a smooth quasi-periodic function,we prove the boundedness of all solutions and the existence of quasi-periodic solutions for the equation by canonical transformations and the invariant curve theorem for smooth quasi-periodic twist mappings.

关 键 词：DUFFING方程 拟周期解 扭转映射 不变曲线 

分 类 号：O175.[理学—数学]