Existence and non-existence results for two-point boundary value problems of higher order

We prove existence and non-existence results for two point higher order equation u((n))(t) + f(t, u(t), ..., u((n-1))(t)) = s p(t), (1) for f : [0, 1] x R-n -> R and p : [0, 1] -> R+ continuous functions, s a real parameter with the boundary conditions u((i))(0) = 0, for i =0, n-3, a u((n-2))(0) - b u((n-1))(0) = A, (2) c u((n-2))(1) + d u((n-1))(1) = B, with a, c, A, B is an element of R and b, d >= 0 such that a(2) + b > 0 and c(2) + d > 0. The proof makes use of a priori estimates, lower and upper solutions technique and coincidence degree theory.