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.