Abstract

In this paper we introduce the notion of (h, k) dichotomy spectrum for systems of nonautonomous linear differential equations with impulse effect. This new kind of spectrum is based on the notion of (h, k) dichotomies and consists of a union of disjoint closed intervals. The spectral intervals and associated spectral manifolds generalize the concept of eigenvalues and eigenspaces of an autonomous differential equation i = Ax without impulse. The main result of this paper is a spectral theorem which describes all possible forms of the (h, k) dichotomy spectrum. Examples of spectra in the scalar case as well as some inclusion properties are given.