The Relationship between Various Types of Dichotomy / R. A. Prokhorova

Abstract

We consider linear systems of the form dx/dt = A(t)x (1) with piecewise continuous coefficients A(·) : [0, +∞) → Hom (Rn, Rn) and principal solution matrix X(t), X(0) = E. In the following, we identify system (1) with the coefficient matrix A(·) and refer to it as the system A. The aim of the present paper is to study the relationship between the sets ED, L∞D, and LpD of linear systems (1) that have the exponential, ordinary, and Lp dichotomy, respectively. We use the following well-known definitions of these dichotomies.