一类三阶三点边值问题正解的存在性

Existence of Positive Solutions for a Third-order Three-point Boundary Value Problem

文章研究了一类三阶三点边值问题u″′(t)=a(t)f(t,u(t)),u(0)=δu(η),u″(1)=0,u′(1)=0两个正解的存在性,首先给出该边值问题的格林函数,将边值问题的解的存在性转化为一个积分算子的不动点的存在性,在适当的Banach空间中定义了一个锥,然后结合格林函数的性质,利用Krasnoselskii不动点定理研究了该边值问题正解的存在性,给出了两个正解存在的充分条件。

We study the existence of two positive solutions for the third-order three-point boundary value problem,u″′（t）=a（t）f（t,u（t））,u（0）=δu（η）,u″（1）=0,u′（1）=0,the corresponding Green＇s function is given,we convert the existence of solutions for the boundary value problem into the existence of fixed point of an integral operator equation.A cone on a Banach space is well defined,by using Krasnoselskii＇s fixed point theorem combined with the properties of Green function,we establish sufficient conditions for the existence of two positive solutions to the boundary value problem.