关键词: 反周期和非线性边界条件；藕合上下解；单调迭代法；具有分段常数变量微分方程；最小最大解.

Abstract:

The authors employ the method of upper and lower solutions coupled with  the monotone iterative technique to obtain results of existence and
 uniqueness for anti periodic  and nonlinear boundary problems of  differential equations with piecewise constant arguments x′(t)=f(t,x(t),x(［t-k］)), x(0)+h(x(T))=0\$, where \$h(θ)∈C^1(R),h′(θ)>0.

Key words: Anti periodic boundary conditions and nonlinear boundary conditions, Monotone iterative technique, Lower and upper related solutions, Differential equations with piecewise constant arguments, minimal and maximal solutions