Limit point characteristics of even ordered differential operators

exists and is continuous for n < i with In l977 Robert Kauffman proved for N = 3, L is not always limit point. The purpose of this paper is to investigate the above conjecture for N > 3 and expand Kauffman's work on the N = 2 or fourth order case.

The study revealed that for all N > 3 where

M(y)= (-1)N(xαy(N)(N) Bx α-2N there are real numbers α > 2N + 1 and B > 0 such that M is not limit point. In the fourth order case we studied particularly the equation L(y) = (ry^)^+ (qy) + py with r > 0, q < 0, and p ≥ 0.

The study revealed for L with p = q"/2 + q2/4r > 0, L is disconjugate on [1,∞).

point on [1,∞).

Finally, application of limit point theorems revealed for r = x", where λ > 0, L is limit point on [1,∞) provided any of the following conditions hold:

(i) B < α + 1 and (α < 1 or λ > B - 2) and λ > α - 4 (ii) α < B + 2 and λ > α - 4

(iv) (iii) + 2 and λ < 2B - α 2 and α < 4