Existence results for a fourth-order ordinary differential equation with a four-point boundary condition

The fourth-order differential equation y(4)(t)−f(t,y(t),y″(t))=0,0≤t≤1, with the four-point boundary value problem y(0)=y(1)=0,y(0)=y(1)=0,ay″(ξ1)−by‴(ξ1)=0,cy″(ξ2)+dy‴(ξ2)=0 is studied in this work, where 0≤ξ1<ξ2≤10≤ξ1<ξ2≤1. Some results on the existence of at least one positive solution to the above four-point boundary value problem are obtained by using the Krasnoselskii fixed point theorem.