The method of upper and lower solutions for a Lidstone boundary value problem

In this paper we develop the monotone method in the presence of upper and lower solutions for the 2nd order Lidstone boundary value problem u((2n))(t) = f(t, u(t), u" (t),..., u((2(n-1)))(t)), 0 < t < 1, u((2i))(0) = u((2i))(1) = 0, 0 <= i <= n-1, where f : [0, 1] x R-n -> R is continuous. We obtain sufficient conditions on f to guarantee the existence of solutions between a lower solution and an upper solution for the higher order boundary value problem.