Monotone iterative technique and positive solutions of Lidstone boundary value problems

The purpose of this paper is to investigate the existence and iteration of N symmetric positive solutions for Lidstone boundary value problem: (-1)(n)w((2n))(t) = f(t, w(t)), 0 less than or equal to t less than or equal to 1, w((2f))(0) = w((2f))(1) = 0, 0 less than or equal to i less than or equal to 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. (C) 2002 Elsevier Science Inc. All rights reserved.