Positive solutions of four-point boundary value problem for fourth order ordinary differential equation

In this paper, the fourth order differential equation with four-point boundary value problem y(4)(t)−f(t,y(t),y′′(t))=0,0≤t≤1,y(0)=y(1)=0,y(0)=y(1)=0,ay′′(ξ1)−by′′′(ξ1)=0,cy′′(ξ2)+dy′′′(ξ2)=0 is studied, where 0≤ξ1<ξ2≤10≤ξ1<ξ2≤1. Some sufficient conditions guaranteeing the existence of positive solution to the above four-point boundary value problem are obtained by using the Krasnosekii fixed point theorem.