用摄动法求解一类小参数方程的近似周期解  

Using the Perturbation Method to Solve the Approximate Periodic Solutions for a Small Parameter Equation

作　　者：侯宗毅[1] 许莉[2] 冯春华[2] 

机构地区：[1]河池学院数学系,广西宜州546300 [2]广西师范大学数学学院,广西桂林541004

出　　处：《钦州学院学报》2008年第3期20-23,共4页Journal of Qinzhou University

基　　金：广西教育厅科研基金资助(200708LX163)

摘　　要：主要讨论了强非线性拟保守自治系统+g(x)=εf(x,)的近似周期解及其稳定性,并应用以能量函数为基础的摄动法,分析了两个强非线性方程的近似周期解.实例表明,该摄动法不仅有效而且结果精度较高.The article mainly discuss the existence and the stability of the approximate periodic solutions for strongly nonlinear quasi-conservative autonomous systems x ＋ g（x） = εf（ x, x ）. Furthermore it analyzes the approximate periodic solutions of two strong nonlinear equations by the perturbation method. Examples show that the perturbation method is both effective and high accurate for strongly nonlinear quasi-conservative autonomous systems.

关 键 词：摄动法 强非线性拟保守自治系统 小参数方程 近似周期解 稳定性 

分 类 号：O175[理学—数学]