中文摘要：

文章通过运用上下解的方法证明了一类带有周期边值条件的不连续泛函微分方程解的存在性.并且采用不连续的上下解显著扩大了上下解的选择范围.进而,通过构造具有一致收敛性的上下解的单调迭代序列,得到了该周期边值问题的极值解,即最大、小解.

英文摘要：

This paper is devoted to investigating the existence of solutions for discontinuous functional differential equations with periodic boundary value conditions.By employing the method of upper and lower solutions,which are less than continuous functions,some existence results are obtained.Furthermore,we also develop a monotone iterative technique for obtaining extremal solutions which are obtained as the limits of monotone sequences.