Positive solutions of a nonlinear nth order boundary value problem with nonlocal conditions

We discuss the existence of positive solutions of a nonlinear nth order boundary value problem u(n)+a(t)f(u)=0,t∈(0,1)u(0)=0,u′(0)=0,…,u(n−2)(0)=0,αu(η)=u(1), where 0<η<1, 0<αηn−1<1. In particular, we establish the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem in cones due to Krasnoselkiǐ and Guo.