On the oscillation of third-order Emden-Fowler type difference equations with unbounded neutral term

Abstract

Some new oscillation results are presented for a class of third-order Emden-Fowler difference equations with unbounded neutral coefficients of the form some new oscillation results are presented for a class of third-order Emden-Fowler difference equations with unbounded neutral coefficients of the form
Δ(a(n)(Δ²u(n))^{α})+f(n)y^{λ}(n-τ)=0, where u(n)=y(n)+b(n)y(n-σ), and α, λ are ratio of odd positive integers.The main results are obtained by comparing the studied equation to two first-order quasi-linear delay difference equations. Two additional results are obtained by the Riccati transformation technique. Examples are provided to illustrate the importance of the main results.