Non-oscillation of a class of third order nonhomogeneous difference equations

Abstract

Sufficient conditions, in terms of coefficient functions, are obtained for non-oscillation of a class of linear third order non-homogeneous difference equations of the form y(n + 3) + α (n)y(n + 2)+β (n)y(n + 1)+γ (n)y(n) =f(n), n ≥ 0, δ3y(n - 1) + a(n) δ2y(n - 1) + b(n)δy(n) + c(n)y(n) = f (n - 1), n ≥ 1 and δ (p(n - 1)δ2y(n - 1)) +q(n)δy(n) +r(n)y(n) = f(n - 1), n ≥ 1, where γ (n) ≠ 0 and p(n) > 0. The available methods, usually used for the study of difference equations, are developed appropriately for this purpose.