Three positive solutions for a nonlinear nnth-order mm-point boundary value problem

In this paper, we consider the existence of at least three positive solutions for the nonlinear nnth-order mm-point boundary value problem {u(n)(t)+f(t,u)=0,t∈(0,1),u(0)=0,u′(0)=⋯=u(n−2)(0)=0,u(1)=∑i=1m−2kiu(ξi), where n≥2,ki>0(i=1,2,…,m−2),0<ξ1<ξ2<⋯<ξm−2<1. The associated Green’s function for the nnth-order mm-point boundary value problem is first given, and growth conditions are imposed on the nonlinearity ff which yield the existence of multiple positive solutions by using the Leggett–Williams fixed point theorem.