Positive solutions of the three-point boundary value problem for second order differential equations with an advanced argument

In this paper, by using the fixed point index method, we establish the existence of at least one or at least two positive solutions to the three-point boundary value problem for a second order differential equation with an advanced argument u″(t)+a(t)f(u(h(t)))=0,t∈(0,1),u(0)=0,αu(η)=u(1), where η∈(0,1),α>0,η∈(0,1),α>0, and 1−αη>01−αη>0. As an application, we also give an example to demonstrate our result.