带导数的三阶三点边值问题正解的存在性

Positive Solution for Third-order Three-point Boundary Value Problems with Derivative Dependence x'

应用锥上的不动点指数理论,讨论三阶微分方程边值问题x′′′(t)-a(t)f(t,x(t),x′(t))=0,0<t<1x(0)=x′(η)=x″(1)=0的正解的存在性。式(1)中,η∈[1/2,1]是一个常数。

Using the theory of fixed point index, the existence of solutions for the third-order boundary value problems{x^m（t）-a（t）f（t,x（t）,x＇（t））=0,0〈t〈1 x（0）=x＇（η）=x″（1）=0 are presented ,where η is constant.