时间周期线性扰动系统零解的稳定性分析

研究周期线性扰动系统的零解稳定性。通过对周期线性系统性质的研究,可使用寻找非奇异可微周期矩阵的方法,将对周期线性系统性质的研究转化为对常系数线性系统性质的研究,并将常系数线性扰动系统的零解稳定性结论推广至周期线性扰动系统。在一定条件下,当周期线性扰动系统的扰动项是关于||x||的高阶无穷小时,周期线性扰动系统与未扰动系统的零解具有相同的稳定性。最后,给出了文中所得结果的一个应用举例。

ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR NONLINEAR SYSTEM WITH MULTIPLE DELAYS

The existence of T_periodic solutions of the nonlinear system with multiple delays is studied. By using the topological degree method, sufficient conditions are obtained for the existence of T_periodic solutions. As an application, the existence of positive periodic solution for a logarithmic population model is established under some conditions.