Solutions of Lidstone BVPs for higher-order impulsive differential equations

In this paper, the Lidstone boundary value problems for 2n-order impulsive differential equation x((2n)) (t) = f(t, x(t), x'(t),...,x((2n-1))(t)), 0 < t < 1, Delta x((i)) (s(k)) = I-i,I-k(x(s(k)(-)),...,x((2n-1))(s(k)(-)), i = 1,...,2n - 1, k = 1,...,p with one of following boundary conditions x((2i))(0) = x((2i))(1) = 0, i = 0,...,n - 1 and x((2i+1))(0) = x((2i))(1) = 0, i = 0,..., n-1 are considered. Sufficient conditions which guarantee the existence of at least one solution for these problems are established. The results are new. Examples illustrate our main results. (c) 2004 Elsevier Ltd. All rights reserved.