Abstract :
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.
2005 Elsevier Inc. All rights reserved.
