一类非线性微分方程周期解的研究

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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。
- 四阶非线性系统 /
- 周期解 /
- 存在唯一性 /
- 渐近稳定
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.
- fourth-order nonlinear system /
- periodic solution /
- existence and uniqueness /
- asymptotic stability

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