一类非线性Duffing方程概周期解的存在性  

Existence of Almost Periodic Solutions for Some Nonlinear Duffing Equations

作　　者：张留伟[1] 徐远通[1] 

机构地区：[1]中山大学数学与计算科学学院,广东广州510275

出　　处：《中山大学学报（自然科学版）》2010年第4期6-10,共5页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金资助项目(10471155;10871213)

摘　　要：研究了一类广义非线性Duffing方程概周期解的存在性。通过Lyapunov函数建立辅助线性方程的指数型二分性,在此基础上,选取适当的函数空间,利用不动点定理,得到广义非线性Duffing有界解的存在性,再次利用Lyapunov函数,得到其概周期解的存在性和模包含关系。The existence of almost periodic solutions of some more generalized nonlinear Duffing equations is studied.Firstly,by means of the Lyapunov functions,the exponential dichotomy of the auxiliary linear equations is established.Then,by combining the fixed point theorem in some suitable space,using the Lyapunov function again,the existence of almost periodic solutions of the nonlinear Duffing equations and module inclusion are obtained.

关 键 词：DUFFING方程 概周期 指数型二分性 LYAPUNOV函数 

分 类 号：O175.14[理学—数学]