Systems of linear impulsive differential equations

摘要

In this chapter, some results of Chapter 1 for the general linear boundary value problem we realize for the following impulsive differential systems dx dt = P(t)x + q(t) for a.a. t ∈ I T, (5.1.1) x(τl+) ? x(τl?) = G(τl)x(τl) + u(τl) (l = 1, 2, . . .); (5.1.2) ?(x) = c0, (5.1.3) where P ∈ L(I; Rn×n), q ∈ L(I; Rn), G ∈ B(T; Rn×n), u ∈ B(T; Rn), T = {τ1, τ2, . . . }, τl ∈ I (l = 1, 2, . . .), τl = τk if l = k (l, k = 1, 2, . . .), ? : BV∞(I; Rn) → Rn is a linear bounded vectorfunctional, and c0 ∈ Rn. Everywhere we assume that I = [a, b].