We first consider (-1)[sup n-1]y[sup (n)](t) = f(y(t)), 0 ≤ t ≤ 1, satisfying the (1, n - 1) right focal boundary conditions y(0) = 0 = y[sup (i)](1), 1 ≤ i ≤ n - 1 where f : R → [0, ∞) is continuous. Best possible upper and lower bounds are obtained on the integral of the Green's function associated with this problem. These bounds are then used in conjunction with growth assumptions on f to apply the Leggett-Williams Fixed Point Theorem to obtain the existence of at least three positive solutions. We then generalize these results to the (k, n - k) right focal problem (-1)[sup n-k]y[sup (n)](t) = f(y(t)), 0 ≤ t ≤ 1, y[sup (i)](0) = 0 = y[sup (j)](1), 0 ≤ i ≤ k - 1, k ≤ j ≤ n - 1.
