Two-Point Problem for Higher-Order Systems

In this note we prove an existence theorem for the two-point problem m 1 uŽm.Žt. fŽt, uŽt., . . . ,uŽm 1.Žt.. Ý t k k for all t a, b k 0 uŽ k.Ža. uŽ k.Žb. 0 for all k 0, . . . , m 1, where f : a, b Rnm Rn is a given function and 0, . . . , m 1 are suitable vectors of Rn. In particular, we extend a result recently obtained for the case m 1.