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

作　　者：王培光[1] 黄倩[2] 

机构地区：[1]河北大学电子信息工程学院,保定071002 [2]河北大学数学与计算机学院,保定071002

出　　处：《工程数学学报》2011年第4期532-536,共5页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10971045);教育部重点科研项目(207014);河北省自然科学基金(A2009000151)~~

摘　　要：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.

关 键 词：时标 脉冲动力方程 周期边值问题 拟线性化方法 高阶收敛 

分 类 号：O175.1[理学—数学]