一类非线性非自治系统周期解的研究

Periodic Solutions to a Class of Nonlinear Nonautonomous Systems

研究了一类非线性非自治周期系统周期解存在唯一性及其渐近稳定性．采用类比缓变系数的方法，作出了相应的Liapunov函数，对缓变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．

We study the existence, uniqueness and asymtotic stability of the periodic solutions to a class of the nonlinear nonautonomous periodic systems.We find the relevant Liapunov function by using the method of analogical slowly-changing coefficients. We also give a comparatively ac- curate estimation of the slowly-changing coeffcients and offer the suffcient conditions which guarantee the existence, uniqueness and asymptotic stability of the periodic solutions.