Global existence results for impulsive differential equations

This paper studies the global existence of solutions of the impulsive differential equation{x′(t)=f(t,x(t)),t⩾0,t≠τk,Δx(t)=Ik(x(t)),t=τk,k=1,2,…, where Δx(t)=x(t+)−x(t), f:[0,∞)×Rn→Rn, Ik:Rn→Rn, k=1,2,…, and {τk} is a sequence of real numbers such that 0<τ1<τ2<⋯<τk→∞ as k→∞. Some interesting results on global existence of solutions are established even though the corresponding continuous equation, i.e., y′(t)=f(t,y(t)), may not have global existence of solutions.