On the positive solutions of Lidstone boundary value problems

The existence, nonexistence and multiplicity of positive solutions are considered for Lidstone boundary value problem: (- 1)(n)omega((2n)) = lambdaf (t, omega(t)), 0 less than or equal to t less than or equal to 1, omega ((2i))(0)= omega((2i))(1) = 0 less than or equal to i less than or equal to n - 1, where lambda > 0. By making use of Krasnosel'skii fixed point theorem, some new results are obtained. Particularly, it is proved that the Lidstone boundary value problem has N positive solutions under suitable conditions, where N is an arbitrary natural number. (C) 2002 Elsevier Science Inc. All rights reserved.