二阶含逐段常变量微分方程的渐近概周期解

The asymptotically almost periodic solution of two order differential equation with piecewise constant argument

具有逐段常变量微分方程是连续和离散动力系统的混合体,具有微分方程和差分方程的双重性质。利用压缩映射不动点理论并构造差分方程的渐近概周期序列解,讨论了一类二阶含逐段常变量微分方程的渐近概周期解的存在性,得到这类方程有渐近概周期解存在的充分条件。

The differential equation with piecewise constant argument combines the continuous dynamic system and the discrete dynamic system. It has the dual nature of differential equation and difference equation. By using the fixed point theorem and constructing asymptotically almost periodic sequence solution for difference equation, the ex- istence of asymptotically almost periodic solution of two order differential equation with piecewise constant argument is discussed, and the sufficient conditions for the existence of the asymptotically almost periodic solution are given.