摘要
用上下解方法研究了三阶非线性微分方程四点边值问题ｕ＝ｆ（ｔ，ｕ，ｕ″），ａ≤ｔ≤ｂ，ｕ（ａ）＝ｕ（ａ０），ｕ′（ａ）－δｕ″（ａ）＝Ａ，ｕ（ｂ）＝ｕ（ｂ０），｛其中ａ＜ａ０≤ｂ０＜ｂ，δ≥０，Ａ是给定常数．证明了ｆ在适当条件下，上述边值问题有解的充要条件是存在一个下解α和上解β使得α（ｔ）≤β（ｔ），ａ≤ｔ≤ｂ．
A four point boundary value problem for nonlinear third order differential equation u=f(t,u,u″), a≤t≤b, u(a)=u(a 0), u′(a)-δu″(a)=A, u(b)=u(b 0), is studied by using the generalized method of upper and lower solutions, where a<a 0≤b 0<b, δ≥0,A is a given real number. Under suitable conditions of f, the problem has a solution if and only if there exist a lower solution α and an upper solution β with α≤β for a≤t≤b.
出处
《纯粹数学与应用数学》
CSCD
1998年第3期40-45,共6页
Pure and Applied Mathematics
基金
黑龙江自然科学基金
关键词
微分方程
四点边值问题
上下解
非线性
边值问题
third order differential equation
four point boundry value problem
lower and upper solutions method
