Global existence results for impulsive functional differential equations

In this paper, we investigate the existence of solutions of impulsive delay differential equation{x′(t)=f(t,xt),t⩾0,t≠τk,k∈N,Δx(t)=Ik(x(t)),t=τk,k∈N. New global existence theorems are established without assuming the global existence of solutions of the corresponding continuous equation.