集值控制微分方程解的广义拟线性方法  

Generalized quasi-linearization for a class of set control differential equations

作　　者：王培光[1] 刘静[2] 李志芳[1] 

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：《黑龙江大学自然科学学报》2011年第2期148-151,共4页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(10971045);河北省自然科学基金资助项目(A2009000151)

摘　　要：讨论一类集值控制微分方程的初值问题,研究其解的收敛性。利用上下解方法及单调迭代技巧构造了两个逼近解序列,并说明这两个逼近解序列一致收敛到给出的初值问题的解,同时运用广义拟线性方法及Gronwall不等式技巧,获得了解序列平方收敛于该问题的解的结果。The initial value problem for a class of set control differential equations is discussed.The convergence of the solution is presented.In the course of the study,upper-lower solution method and monotone iterative technique is employed to construct two approximate solution sequences.It is shown that those two approximate solution sequences both converge uniformly to the solution of the given problem.Furthermore,by using the generalized quasi-linearization and Gronwall inequality,it is proved that the solution sequences converge quadratically to the solution of the given problem.

关 键 词：集值控制微分方程 广义拟线性化方法 平方收敛 

分 类 号：O175.1[理学—数学]