摘要
本文讨论了指数型三分性的粗糙度,得到主要结果如下: 设A(t)是R上连续有界的n阶方阵函数,如果微分系统(dx)/(dt)=A(t)x在R上具有指数型三分性,其常数为K≥1,α>0,投影为P_+、P_-,则对于任何满足‖B(t)‖<(α/(2K))的连续有界n阶方阵函数B(t),摄动系统(dx)/(dt)=[A(t)+B(t)]x在R上具有投影为P_+(B)和P_-(B)的指数型三分性,并且 秩(P_+(B))=秩(P_+),秩(P_(B))=秩(P_-)。
In this paper we discuss the roughness of exponential trichotomy of differential systems, obtain the main result as follows:Let A(t), B(t) be n ×n matrix functions, bounded and continuous on R, the differential system x'(t) - A(t)x(t) have an exponential trichotomy (on R) with constants K ≥ 1,α> 0 and projections P+, P- . If |B(t)| <α/2K(t∈R), then the perturbed system x '(t) = [A(t) + B(t)]x(t) has an exponential trichotomy (on R) with projections P+ (B). P-(B), and rankP+ (B)=rankP+ , rankP- (B) = rankP- .
出处
《工程数学学报》
CSCD
1993年第4期55-60,共6页
Chinese Journal of Engineering Mathematics
