Existence and uniqueness of positive solutions for an integral boundary value problem

This paper deals with the existence and uniqueness of positive solutions for the second-order integral boundary value problem {u″+f(u)=0,u(0)=∫01u(τ)dα(τ),u(1)=∫01u(τ)dβ(τ), where f∈C(R,R)f∈C(R,R) is sign-changing. The main tools used in the proofs are the a priori estimate method and the Leray–Schauder fixed point theorem.