Existence results for n-point boundary value problem of second order ordinary differential equations

This study concerns the existence of positive solutions to the boundary value problemu″+a(t)f(u)=0,t∈(0,1),u′(0)=∑i=1n-2biu′(ξi),u(1)=∑i=1n-2aiu(ξi),where ξi∈(0,1) with 0<ξ1<ξ2<⋯<ξn-2<1, ai, bi∈[0,∞) with 0<∑i=1n-2ai<1 and ∑i=1n-2bi<1. By applying the Krasnoselskii's fixed-point theorem in Banach spaces, some sufficient conditions guaranteeing the existence of at least one positive solution or at least two positive solutions are established for the above general n-point boundary value problem.