Eventual disconjugacy of self-adjoint difference equations

Given an eventually disconjugate second-order self-adjoint difference equation Δ(cnΔ n) + an n+1 = 0, where cn ≠ 0 and is not assumed to be positive, this paper studies the eventual disconjugacy of the perturbed difference equation Δ(cnΔyn) + (an + fn)yn+1 = 0. Analogous to a theorem of Willett for corresponding differential equations, a necessary and sufficient condition for eventual disconjugacy in terms of a convergent sequence of averaged sums of fn is obtained.