Positive solutions of nth order m-point boundary value problem

In this paper, we study the existence of positive solutions of nth order m-point boundary value problemu(n)(t)+a(t)f(u(t))=0,t∈(0,1),u(0)=u′(0)=⋯=u(n-2)(0)=0,u(1)=∑i=1m-2αiu(ηi),where n⩾2, m>2, 0<η1<η2<⋯<ηm-2<1,αi>0(i=1,2,…,m-2) with ∑i=1m-2αiηin-1<1. We obtained the existence of positive solutions by using the fixed point theorems of cone expansion and compression of norm type. The results obtained in this paper essentially improve and generalize some well-known results.