随机脉冲泛函微分方程的p阶矩有界性

p-Moment Boundedness of Functional Differential Equations with Random Impulses

随机脉冲泛函微分方程是一个具有广泛应用前景的数学模型.该文利用带Razumikhin条件的Liapunov直接法和比较原理,得到了随机脉冲泛函微分方程的解的一致(一致且最终、一致且一致最终)p阶矩有界的充分条件,其中在获得一致有界性和一致最终有界性时,对dV(t,x(t))/dt的限制条件也较少,因此研究结果非常便于应用.

Random impulsive functional differential equation is a mathematical model with extensive applications. By means of Liapunov＇s direct method coupled with Razumikhin technique and comparison principle, some sufficient conditions for uniformly （uniformly and ultimately, uniformly and uniformly ultimately） p-moment boundedness of such systems are presented, where dV（t,x（t）） /dt is imposed only on a little restriction even to obtain uniform boundedness and dt uniformly ultimate boundedness. Thus the obtained results are very convenient to apply.