一类非线性系的渐近稳定概周期解

The asymptotic stable almost periodic solution for a class nonlinear system

讨论一类概周期系数非线性方程,就其概周期解的存在性、唯一性、稳定性等问题与线性方程系进行比较研究.通过证明发现非线性系具有线性方程系的4条主要性质,且证明了在小指数扰动情况下,非线性系的概周期解仍然保持渐近稳定.

In this paper, we investigate a class nonlinear system with almost periodic coefficient and dis- cuss existence, uniqueness and stability of the almost periodic solution. The results show that the four properties of linear system can be also applied to the nonlinear system. We also prove that in a small index perturbation case almost periodic solutions for nonlinear system remains asymptotically stable.