三阶非线性微分方程边值问题正解的存在性

Existence of positive solutions for nonlinear third-order ordinary differential equations

本文应用锥上的不动点定理研究了三阶四点边值问题{u'''(t)+f(t,u(t))=0,t∈[0,1],u′(0)=αu(ξ),u′(1)+βu(η)=0,u″(0)=0正解的存在性,其中α和β是正的参数,0≤ξ≤η≤1.在f满足适当的增长条件下,本文通过对核函数的上下界估计获得了该问题正解的存在性.

In this paper, by applying the fixed point theorem in cone, we study the existence of positive solutions of third-order four-point boundary value problem{um（t）＋f（t,u（t）_=0,t∈[0,1],u（0）=αu（ξ）,u（1）＋βu（η）=0,un（0）=0 where α and/ βare positive parameters, 0≤ξ≤η≤1. Under some conditions on f, we obtain the existence of positive solutions of the problem by estimating the upper bounds and lower bounds for kernel function.