EXISTENCE OF SOLUTIONS FOR HIGH ORDER ORDINARY DIFFERENTIAL EQUATIONS WITH SOME PERIODIC-TYPE BOUNDARY CONDITION

We consider the following high order periodic-type boundary value problem (PBVP) {(E)u((n)(t)) = f(t,u(t), u((1)) (t),...u((n-2)) (t), u((n-1)) (t)) for t epsilon (0, T) (PBC) {u((i)) (0) = 0, 0 <= i <= n - 3, u((n-2))(0) = u((n-2))(T), u((n-1))(0) = u((n-1)) (T), where f epsilon C([0, T] x R-n, R), n >= 2 and satisfies the so-called Nagumo's condition. hi this article, we will use a general upper and lower solution method to establish an existence theorem for solutions of (PBVP).