时标上脉冲动力方程周期边值问题的拟线性化方法

Quasilinearization Method for Impulsive Dynamic Equations with Periodic Boundary Value Problems on Time Scales

本文研究了一类时标上脉冲动力方程周期边值问题解的收敛性问题.利用时标上一阶脉冲动力不等式﹑上下解和单调迭代技巧证明了该问题解的一致收敛性结果,并进一步采用拟线性化方法和分析技巧获得了该方程在周期边值条件下两个逼近解序列高阶收敛的充分性判据.本文所得结果发展了时标上动力方程定性理论的结果.

In this paper, the convergence of the solution to a class of periodic boundary value problem of impulsive dynamic equations on time scales is investigated. By using first-order impulsive dynamic inequality on time scales, the upper and lower solution method and the monotone iterative technique, the uniform convergence of this problem is proved. Meanwhile, by utilizing the quasilinearization method and analytical technique, some sufficient criteria for the rapid convergence of two sequences of approximate solution are obtained on the periodic boundary value condition. Our results extend several known results of qualitative theory of dynamic equations on time scales.