一类一阶脉冲微分方程积分边值问题

考虑具有两个函数差的一阶脉冲微分方程积分边值问题极值解的存在性,通过上下解方法和单调迭代技术得到了边值问题存在耦合极大解(-β)和极小解(-α)的充分条件.利用脉冲微分不等式理论,给出了边值问题存在唯一解,即α=β的充分条件.本文结果包含了具有两个函数差的常微分方程初值问题(当Ik=Gk=0,λ1=λ2=0时),常微分方程积分边值问题(当Ik=Gk=0,g=0,λ1=0,λ2=±1时),一阶脉冲微分方程反周期边值问题(当g=0,Gk=0,λ2=d=0时)的相关结果.

Integral Boundary Values of Category- Ⅰ First-Order Impulsive Differential Equation

A research has been made on the existence of extreme solutions to first-order impulsive differential equations with difference between two functions.By employing the approaches for upper and lower solutions and monotone iterative technique,the authors have obtained the sufficient conditions for the existence of coupled maximal solution and minimal solution.Then by using the theory of impulsive differential inequality,the authors have presented the unique solution to the boundary problem.The researches in this paper have offered solutions to initial value problem for ordinary differential equation involving difference of two monotone functions,ordinary differential equation with integral boundary conditions,and first-order impulsive ordinary differential equation with anti-periodic.