Monotone iterative technique and positive solutions of Lidstone boundary value problems

摘要

The purpose of this paper is to investigate the existence and iteration of N symmetric positive solutions for Lidstone boundary value problem:(−1)nw(2n)(t)=f(t,w(t)),0⩽t⩽1,w(2i)(0)=w(2i)(1)=0,0⩽i⩽n−1.By making use of monotone iterative technique, we are proved that the Lidstone boundary value problem has N symmetric positive solutions under suitable conditions, and given the iterative method for approximating to these solutions, where N is a natural number.