一类非线性微分方程周期解的研究
Research of the Periodic Solution for a Class of Nonlinear Differential Equations
-
摘要: 本文研究了一类最普遍的四阶非线性非自治系统的周期解的存在唯一性与渐近稳定性。我们采用了类比缓交系数的方法,作出了相应的Liapunov函数,对缓交系数作了较为精确的估计,得到了存在唯一渐近稳定的周期解的充分条件。Abstract: In this paper,we study the existence,uniqueness and asymptotic stabgility of the periodic solution for a class of the most,universal fourth-order nonlinear nonautonomous periodic systems.We give the relevant Liapunov function by using the method of analogical slowly changing coefficients.We also give a considerably accurate estimation of the slowly changing coefficients and obtain the sufficient conditions which guarantee the existence,uniqueness and asymptotic Stability of the periodci solutions.
-
[1] Wong Rongliang,Existence and stability of periodic solutions for a class of nonlinear and nonautonomy system of three orders,Kexue Tongbao,32,16(1987). [2] 金均,具有缓变系数非线性周期系统周期解的存在唯一性,数学研究与评论,11(2)(1991). [3] 金均,一类非线性系统周期解的存在唯一性及其稳定性,上海师范大学学报,22(1)(1993), [4] 秦元勋、王联、王慕秋.《运动稳定性理论和它的应用》,科学出版社(1981), [5] 王联、王慕秋,高阶非线性周期系统沟周期解,微分方程年刊,3(1)(1987). [6] J.Lasall and S.Lefschetz,Stabilim by Liapunov's Direct Method ,with Application,Academic Press,New York,(1961),66. -
点击查看大图
计量
- 文章访问数: 2167
- HTML全文浏览量: 58
- PDF下载量: 485
- 被引次数: 0
下载:
