Multiple positive solutions for second-order m-point boundary value problems

In this paper, the second-order m-point boundary value problemu″(t)+f(t,u)=0,0⩽t⩽1,u(0)=0,u′(1)−∑i=1m−2kiu′(ξi)=0 is studied, where ki>0ki>0(i=1,2,…,m−2)(i=1,2,…,m−2), 0<ξ1<ξ2<⋯<ξm−2<10<ξ1<ξ2<⋯<ξm−2<1. We give at first the associated Green's function and its properties for the m-point boundary value problem, and growth conditions are imposed on f which yield the existence of at least three positive solutions by using the five functionals fixed point theorem and the properties.