一阶常微分方程初值问题的上、下解与拟上下解的存在定理

利用上、下解与拟上下解方法讨论常微分方程问题时,文献均足假没上、下解与拟上下解是存在的,进而讨论方程的解．文章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．

The Existence Theorem of the Upper and Lower Solutions and the Quasi- upper and Lower Solutions for One- order Ordinary Differential Equations

The existence of the upper and lower solutions and the quasi -upper and lower solutions is usually assumed in literature when it comes to the handling of ordinary differential equations by means of the above two solutions. This paper discusses the existence theorem of the upper and lower solutions and the quasi - upper and lower solutions of the initial value problem. It holds that the given existence theorem provides adequate grounds on which the upper and lower solutions and the quasi - upper and lower solutions can be employed to solve the initial value problem of one - order ordinary differential equations.