论文标题
线性差异系统的分裂特性与较小的延迟
Splitting properties of linear differential systems with small delays
论文作者
论文摘要
我们研究了伪指数二分法造成的奇异扰动问题。对于一般的线性非自主智障差分方程，以前的工作确定了伪指数二分法的存在。本文的主要目的是对该二分法的三个分裂特性进行详细分析。通过获得新的新估计值并给出与该二分法相关的边界和指数的明确表达式，我们证明，随着延迟趋于零，光谱间隙接近无穷大，以及与该二分法相关的角度距离和分离指数从下面的正常常数界定，这独立于延迟。
We investigate singular perturbation problems caused by small delays in the view of pseudo-exponential dichotomy. For a general linear non-autonomous retarded differential equation with small delay, previous works established the existence of a pseudo-exponential dichotomy. The main objective of this paper is to give a detailed analysis of three splitting properties of this dichotomy. By obtaining serval new estimates and giving the explicit expressions of the bounds and the exponents associated with this dichotomy, we prove that as the delay tends to zero, the spectral gap approaches to infinity, and the angular distance and the separation index associated with this dichotomy are bounded from below by a positive constant which is independent of the delay.
