一类n维非线性系统的周期解

On The Periodic Solutions of A Class n-Dimensional Nonlinear System

讨论n维周期非线性系统dx/dt=A(t)x+g(t,x)的周期解的存在性。通过应用不动点定理以及讨论解的最终有界性等方法,得到一些关于周期解存在的若干充分条件。

This paper deals with the existence of periodic solutions of n-dimensional periodic nonlinear system dx/dt = A(t)x+g(t ,x) . x∈ERn-in which the vector-value function g(t,x) :R×Rn→R×Rn includes some higher order terms in x∈Rn. By using the fixed point theorems and proving the ultimately boundedness of the solutions .some results on the existence of periodic solution are obtained.