一类微分方程周期边值问题的单调迭代方法

THE MONOTONE ITERATIVE METHOD FOR PERIODIC BOUNDARY VALUE PROBLEM OF SECOND ORDER INTEGRO_DIFFERENTIAL EQUATIONS

研究二阶非线性积分微分方程的周期边值问题：－ｘ″＝ｆ（ｔ，ｘ，ｘ′，Ｔｘ），ｘ（０）＝ｘ（１），ｘ′（０）＝ｘ′（１）解的存在性及唯一性，并说明所得主要结果在高阶微分方程混合问题上的应用．

This paper considered the following periodic boundary value problem for nonlinear integro _differential equation(PBVP) -x″=f(t,x,x′,Tx),x(0)=x(1),x′(0)=x′(1). It obtained the existence and uniqueness of solutions for PBVP,and gived their application in higher order differential equations.