间断概自守函数与具有逐段常数变元的微分方程的概自守解
Discontinuous Almost Automorphic Functions and Almost Automorphic Solutions of Differential Equations with Piecewise Constant Argument
摘要：
本文引入了一类不连续的概自守函数，它在研究具有逐段常数变元的微分方程的概自守解时自然出现。利用它们的基本性质证明了一类具有逐段常数变元的微分方程组有界解的几乎自同构性。由于这些方程的强离散性，得到了一类非自治几乎自守差分系统的唯一离散几乎自守解的存在性，其中指数二分性和离散双几乎自守性是基本条件.
英文摘要：
In this article we introduce a class of discontinuous almost automorphic functions which appears naturally in the study of almost automorphic solutions of differential equations with piecewise constant argument. Their fundamental properties are used to prove the almost automorphicity of bounded solutions of a system of differential equations with piecewise constant argument. Due to the strong discrete character of these equations, the existence of a unique discrete almost automorphic solution of a non-autonomous almost automorphic difference system is obtained, for which conditions of exponential dichotomy and discrete Bi-almost automorphicity are fundamental.
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