三阶非线性微分方程边值问题正解的存在性

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

摘要:

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，β是正的参数，0≤ξ＜η≤1.在f满足适当的增长条件下，通过对核函数得到上下界估计，获得了该问题正解的存在性。

Abstract:

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 problemu'''(t)+f(t,u(t))=0,t∈[0,1],u'(0)=αu(ξ ),u'(1)+βu(η)=0,u''(0)=0,whereα，βare positive parameters,0≤ξ＜η≤1.Under some conditions on f,we obtained the existence of positive solutions of the problem (1.1)by estimating the upper bounds and lower bounds for kernel function.