Existence of positive solutions of Lidstone boundary value problems

We show that there exists at least one positive solution for Lidstone boundary value problem (−1)nu(2n)(t) = f t,u(t),u (t), . . . , u(2(n−1))(t) , 0 < t <1, u(2i)(0) = u(2i)(1) = 0, i= 0, 1, . . . , n−1, under some suitable conditions. Our proof is based upon global bifurcation techniques.  2005 Elsevier Inc. All rights reserved