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

In this paper, by using Krasnoselskiiʹs 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 problem View the MathML sourceu″(t)+λa(t)f(u(t))=0,00am-2>0, ξiξi satisfy 0<ξ1<ξ2<⋯<ξm-2<10<ξ1<ξ2<⋯<ξm-2<1 and View the MathML source∑i=1m-2aiξi<1. We derive an explicit interval of λλ such that for any λλ 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 λλ in an appropriate interval is also discussed.