三阶非线性边值问题正解的存在性

Existence of Positive Solutions for Nonlinear Third-order Boundary Value Problem

研究了一类含参数三阶非线性微分方程边值问题,给出其正解存在的充分条件,利用锥不动点定理并结合Green函数估计,证明了该问题正解的存在性。

The existence of positive solutions for the following nonlinear third-order boundary value problemu″′(t)-ρ^(2)u′(t)=f(t,u(t)),(0<t<1);u′(0)=0,u(1)=0,u″(1)=0.where ρ>0 was a parameter.By means of the fixed point theorem on cones,some existence results of positive solutions were proved.