具有跳跃和时间周期势的Duffing方程的Lagrange稳定性  

Lagrange Stability for Duffing Equation with Jumping Term and Time Periodic Potential

作　　者：李红霞[1] 

机构地区：[1]中国海洋大学数学科学学院,山东青岛266100

出　　处：《中国海洋大学学报（自然科学版）》2014年第11期118-124,共7页Periodical of Ocean University of China

基　　金：山东省自然科学基金项目(ZR2013AM026)资助

摘　　要：本文研究一类具有非对称项和有界扰动项的Duffing方程,推广了王新平在文献[9]中的结论。当扰动项带有时间周期系数时,分别考虑ω为有理数和无理数的情况,对扰动项作出合理的假设后,利用典则变换和Moser小扭转定理的变形,证明了方程的所有解是有界的,即Lagrange稳定性。In this paper, we will study a type of Dulling equation which has asymmetric term and jump- ing nonlinearity. We extend the results of WangEg. When the perturbation term has time periodic coefficient, considering to is rational and irrational number respectively and given some reasonable hypothesis to the perturbation term, we can make use of canonical transformation and the variants of Moser＇s small twist theorem to prove the Lagrange stability of the Duffing equation, namely, all the solutions o{ the e- quation are bounded.

关 键 词：DUFFING方程 LAGRANGE稳定性 扭转定理 

分 类 号：O175.12[理学—数学]