Green’s function and positive solutions of nth order m-point boundary value problem

In this paper, we study the expression and properties of Green’s function for nth order m-point boundary value problem.u(n)(t)+a(t)f(u)=0,t∈(0,1)u(0)=u′(0)=⋯=u(n-2)(0)=0,u(1)=∑i=1m-2αiu(ηi),where 0 < η1 < η2 < ⋯ < ηn−2 < 1, αi > 0 with ∑i=1m-2αiηin-1<1, furthermore, we obtained the existence of positive solutions by meas of fixed point index theory.