The asymptotic behavior of nonoscillatory solutions of nonlinear neutral type difference equations

In this paper, the authors study the asymptotic behavior of solutions of second-order neutral type difference equations of the form Δ 2 ( y n + p y n − k ) + f ( n , y n − ℓ ) = 0 , n ∈ ℕ , n ε, ℕ and Δ 2 ( y n + p y n − k ) + f ( n , y n − ℓ , Δ y n − ℓ ) = 0 , n ∈ ℕ ,n ε ℕ using some difference inequalities. We establish conditions under which all nonoscillatory solutions are asymptotic to an + b as n → ∞ with a and b ε ℕ.