上、下解与拟上下解的存在性  

The Existence Theorem of the Upper and Lower Solutions and the Quasi-Upper and Lower Solutions

作　　者：张骞[1] 

机构地区：[1]陇东学院数学系,甘肃庆阳745000

出　　处：《西安文理学院学报（自然科学版）》2011年第1期8-10,共3页Journal of Xi’an University(Natural Science Edition)

基　　金：甘肃省教育厅科研基金资助项目(0710-04)

摘　　要：利用上、下解与拟上下解方法讨论常微分方程问题时,文献均是假设上、下解与拟上下解是存在的,进而讨论方程的解.给出一阶常微分方程初值问题的上、下解与拟上下解的存在性定理,为利用上、下解与拟上下解方法讨论一阶常微分方程初值问题提供充分的依据.Previous studies of the ordinary differential equations by means of upper and lower solutions and the quasi-upper and lower solutions are based on the assumed existence of the various solutions.In this paper,we get the existence theorem of the upper and lower solutions and the quasi-upper and lower solutions of the initial value problem and thus provide a sufficient basis for studying one-order ordinary differential equations by means of the upper and lower solutions and the quasi-upper and lower solutions.

关 键 词：上、下解 拟上下解 初值问题 周期边值问题 

分 类 号：O177.5[理学—数学]