一类三阶非线性常微分方程边值问题正解的存在性

Existence of positive solutions for a class of boundary value problem of third-order nonlinear ordinary differential equations

本文研究了一类三阶非线性常微分方程边值问题■正解的存在性,其中f∈C([0,1]×R,R)且当|u′|→0时,f(t,u′)=au′+o(|u′|);当|u′|→∞时f(t,u′)=bu′+o(|u′|),a,b∈(0,+∞).主要结果的证明基于Dancer全局分歧定理.

In this paper, we study the existence of the positive solutions of the following boundary value problem of third-order nonlinear ordinary differential equations {u ′′′+λf(t,u′)=0, t∈[0,1], u(0)=u(1)=u″(0)=0, where f∈C([0,1]× R,R), f(t,u′)=au′+o(|u′|) as |u′|→0, f(t,u′)=bu′+o(|u′|) as |u′|→∞, and a,b∈(0,+∞). The proof of the main result is based on the Dancer global bifurcation theorem.