Monotone iterative technique and positive solutions of Lidstone boundary value problems

The purpose of this paper is to investigate the existence 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((2i))(0) = w((2i))(1) = 0, 0 less than or equal to i less than or equal to n - 1 By making use of monotone iterative technique, we established some new results. Particularly, we proved that the Lidstone boundary value problem has N symmetric positive solutions under suitable conditions, and these solutions are obtained by iteration procedures; where N is a natural number. (C) 2002 Elsevier Science Inc. All rights reserved.