四阶非线性周期系统周期解的存在唯一性

Existence and Uniqueness of Periodic Solutions for Fourth-Order Nonlinear Periodic Systems

本文利用Liapunov函数方法,研究了一类具有缓变系数的四阶非线性非自治周期系统的周期解的存在唯一性及其渐近稳定性.我们得到了保证这些系统存在唯一稳定周期解的充分条件,并对系数的缓变范围作了较为精确的估计.

In this paper, we study the existence, uniqueness and stability of the periodic solutions for fourth-order nonlinear nonhomogeneous periodic systems with slowly changing coefficients by using the method of Liapunov Function. We obtain some sufficient conditions which guarantee the existence, uniqueness and asymptotic stability of the periodic solutions of these systems and estimate the extent to which the coefficients are allowed to change.