Two-point problem for higher-order systems

In this note we prove an existence theorem for the two-point problem u((m))(t) = f(t, u(t),...,U(m-1)(t)) + Sigma (m-1)(k=0) t(k)lambda (k) for all t is an element of [a, b] u((k))(a) = u((k))(b) = 0 for all k = 0,..., m - 1, where f: [a, b] x R-nm --> R-n is a given function and lambda (0),..., lambda (m-1) are suitable vectors of R-n. In particular, we extend a result recently obtained for the case m = 1. (C) 2001 Academic Press.