Non-oscillation of solutions of difference equations of third order

In this paper, sufficient conditions in terms of coefficient functions are obtained for non-oscillation of all solutions of a class of linear homogeneous third order difference equations of the form y(n+3)+α(n)y(n+2)+β(n)y(n+1)+γ(n)y(n)=0,n≥0,Δ3y(n−1)+a(n)Δ2y(n−1)+b(n)Δy(n)+c(n)y(n)=0,n≥1, and Δ(p(n−1)Δ2y(n−1))+q(n)Δy(n)+r(n)y(n)=0,n≥1, where γ(n)≠0γ(n)≠0 and p(n)>0p(n)>0. The technique developed depends on non-oscillation of certain linear homogeneous second order difference equations.