Positive solutions of nonlinear second-order m-point boundary value problem

In this paper, by using Krasnoselskii's fixed point theorem of cone expansion-compression type and under suitable conditions, we present the existence of single and multiple positive solutions to the nonlinear second-order m-point boundary value problemu″(t)+λa(t)f(u(t))=0,00, ξi satisfy 0<ξ1<ξ2<⋯<ξm-2<1 and ∑i=1m-2aiξi<1. We derive an explicit interval of λ such that for any λ in this interval, the existence of at least one positive solution to the boundary value problem is guaranteed, and the existence of at least two solutions for λ in an appropriate interval is also discussed.