关于二阶二、三、四点边值问题的上下解方法

The Upper and Lower Solution Method for Some Second Order Two-, Three- and Four-point Boundary Value Problems

运用上下解方法研究二阶边值问题这里0＜α≤b＜1，α，β，γ，δ，ζ，η＞0，A，B均为给定的实数，且ρ：＝αγ＋αδ＋βγ＞0，f为满足Nagumo条件的Caratheodary函数．此问题有解当且仅当有一个上解y和一个下解x，且对所有的0≤t≤1，都有x（t）≤y（t）.

A second order boundary value problem,f is a Caratheodary function satisfying a Nagumo condition, was studied by means of upper and lowersolution method. The problem has solutions if and only if there exists a lower solution x and an uppersolution y and x(t)≤y(t) for all 0≤t≤1.