On Integrable Solutions of Impulsive Delay Differential Equations

The connection of function properties of solutions with exponential stability of linear impulsive differential equation $$\dot{x}(t)-\sum _{k=1}^m{A}_k(t)x[h_k(t)]=r(t),t\ge 0,x(\xi )=\phi (\xi ),\xi <0,$$ $$x({\tau }_j)=B_{j}x({\tau }_j-0),j=1,2,\dots \mathrm{.}$$ The explicit stability results and sufficient conditions for existence of integrable solutions are presented.