一阶时滞微分方程周期边值问题单调迭代法

The periodic boundary value problem for first order differential equations with delay and monotone iterative methods

将用于研究常微分方程周期边值问题地上下解方法与单调迭代技巧,拓展于研究泛函微分方程中一类一阶时滞微分方程周期边值问题,论证了此类方程周期边值问题地最大解和最小解的存在性,以及一致收敛于解地迭代逼近序列.

To find the sufficient conditions for the existence solutions of the periodic boundary value problems of ordinary differential equations, the so called upper and lower solution method together with monotone iterative tech- nique was a very effective strategy. This strategy was applied validly for the first order differential equations with delay without assuming monotonicity in the nonlinear part. Also, two nonotone sequences which converge uniformly to the relevant solutions were obtained.