On Integrable Solutions of Impulsive Delay Differential Equations

Abstract

The connection of function properties of solutions with exponential stability of linear impulsive differential equation $$\dot{x} (t) - \sum_{k=1}^m {A_k (t) x[h_k(t)]} = r(t),~ t \geq 0, x(\xi ) = \varphi (\xi),~ \xi < 0,$$ $$x(\tau_j) = B_j x(\tau_j - 0) , ~j=1,2, \dots .$$ The explicit stability results and sufficient conditions for existence of integrable solutions are presented.