Existence and iteration of positive solutions for a multipoint one-dimensional p-Laplacian boundary value problem

In this paper, we study the existence and iteration of positive solutions for the one-dimensional p-Laplacian differential equation(ϕp(u′(t)))′+q(t)f(t,u(t),u′(t))=0,t∈(0,1),subject to the following multipoint boundary condition,u(0)=∑i=1n-2αiu(ξi),u(1)=∑i=1n-2βiu(ξi).By applying a monotone iterative method, we not only obtain the existence of positive solutions for the problem, but also establish iterative schemes for approximating the solutions.