混合型微分方程的加权伪概周期解

Weighted Pseudo Almost Periodic Solutions to Mixed Type Differential Equation

研究了带有逐段常数变量的混合型微分方程的加权伪概周期解存在唯一性。首先针对具有强迫项的线性微分方程给出了加权伪概周期解存在唯一性的构造性证明,然后利用所得结果再结合不动点方法对非线性扰动方程给出了加权伪概周期解存在唯一性证明。

In this paper, we study the existence and uniqueness of weighted pseudo almost periodic solutions to mixed type differential equations with piecewise constant arguments. We provide a constructing proof for the existence and uniqueness of weighted pseudo almost periodic solutions for a linear equation with forced terms, and then using fixed point method we prove the existence and uniqueness of weighted pseudo almost periodic solutions for the nonlinear perturbed equations.