非线性四阶常微分方程三点边值问题解的存在性及唯一性

Existence and Uniqueness of Solutions of Three-Point Boundary Value Problems for 4th-Order Nonlinear Differential Equations

运用解的匹配法，讨论了非线性四阶常微分方程三点边值问题：ｙ（４）＝ｆ（ｔ，ｙ，ｙ′，ｙ″，ｙ）（１）ｙ（ｉ）（α）＝λｉ，ｙ（ｊ）（β）＝λｊ，ｙ（ｋ）（γ）＝λｋ其中α，β，γ，λｉ，λｊ及λｋ均为实数，解的存在性及唯一性，并且讨论了满足解存在唯一的区间长度的估计。全文总假设函数ｆ（ｔ，ｕ０，ｕ１，ｕ２，ｕ３）在［α，γ］×Ｒ４上连续。

This Paper presents conditions for existence and uniqueness of solutions for certain 4th-order boundary value problems of the form:y (4) =f(t,y,y ′,y ″,y ),y (i) (α)=λ i,y (j) β=λ j,y (k) (γ)=λ k.Where α,β,γ and the λ's are real.It will be assumed throughout this paper that f(t,y,y′,y″,y) is continuous on ×R 4.The approach taken here is based on the use of a solution-matching technique.