常微分方程周期边值问题的一种拟上下解方法

Method of quasi-upper and lower solutions for periodic boundary value problems of ordinary differential equations

为深入探讨常微分方程周期边值问题解的存在性,利用拟上下解方法,获得了一阶和二阶常微分方程周期边值问题拟解对的存在性定理。对于拟上下解反向给定时,亦得到了相应的解的存在性定理。所得结果补充和完善了拟上下解方法。

Aimed at a deeper investigation into the existence of solutions for periodic boundary value problems（PBVP） of ordinary differential equations,this paper offers the existence theorems of coupled quasisolutions for both first order and second order periodic boundary value problems obtained by using the method of quasi-upper and lower solutions.The similar results are also obtained in the case when upper and lower quasisolutions are opposite-ordered.The results complement and perfect the method of quasi-upper and lower solutions.