一类四阶两点边值问题解的存在性的上下解方法

Upper and Lower Solution Method for Fourth-order Two-point Boundary Value Problems

讨论了四阶两点常微分方程边值问题x(4)(t)-λx(t)=f(t,x(t),x″(t))x(0)=x(1)=x″(0)=x(1)=0的解的存在性,其中f:[0,1]×R→R连续,λ>0为常数。利用上下解方法给出了解的存在性结果。

This paper is concerned with the fourth- order ordinary differential equation {x^（4）（t）-λx^m（t）=f（t,x（t）,x″（t）） x（0）=x（1）=x″（0）=x″（1）=0＇ where f：[0,1]×R→Ris continuous and,λ〉0is comtant. Some new existence results are obtained by the upper and lower solution method and the monotone iterative technique.