Second-order Neutral Delay Difference Equations Research Articles

Oscillation and Asymptotic Behavior of Second-Order Neutral Delay Difference Equations with Variable Delays

Oscillation and Asymptotic Behavior of Second-Order Neutral Delay Difference Equations with Variable Delays

Oscillatory Behavior of Quasilinear Neutral Delay Dynamic Equations on Time Scales

By means of the averaging technique and the generalized Riccati transformation technique, we establish some oscillation criteria for the second-order quasilinear neutral delay dynamic equations , , where , and the time scale interval is . Our results in this paper not only extend the results given by Agarwal et al. (2005) but also unify the oscillation of the second-order neutral delay differential equations and the second-order neutral delay difference equations.

Asymptotic behaviour and existence of nonoscillatory solutions of second-order neutral delay difference equations

In this paper, we give a classification of nonoscillatory solution of a second-order neutral delay difference equation of the form Δ2(xn-cnxn-r) = f(n,xg1(n),....,xgm(n)). Some existence results for each kind of nonoscillatory solutions are also established.

Existence of Non-Oscillatory Solutions of Second-Order Neutral Delay Difference Equations

In this paper, we consider the second-order neutral delay difference equation with positive and negative coefficients $$ \Delta r\_n \Delta (x\_n + cx\_{n–k} + p\_{n+1}x\_{n+1–l} = 0 $$ where $c \in \mathbb R, k ≥ 1$ and $m, l ≥ 0$ are integers, $\lbrace r\_n\rbrace^\infty \_{n=n0}, \lbrace p\_n\rbrace ^\infty \_{n=n0}$ and $\lbrace q\_n \rbrace ^\infty \_{n=n0}$ are sequences of non-negative real numbers. We obtain global results (with respect to $c$) which are some sufficient conditions for the existences of non-oscillatory solutions.

Classification and Existence of Non-Oscillatory Solutions of Second-Order Neutral Delay Difference Equations

In this paper, we give a classification of non-oscillatory solutions of a second-order neutral delay difference equation of the form $$ \\Delta^2(xn – c_nx{n–\\tau}) + f (n, x{g_1(n)},..., x{g_m(n)}) = 0 (n ≥ n_0 \\in \\mathbb N). $$ Some existence results for each kind of non-oscillatory solutions are also established.

Oscillation criteria for second-order neutral delay difference equations

In this paper, we establish some oscillation criteria of the second-order delay difference equation Δ [ a n − 1 Δ ( x n − 1 + p n − 1 x n − 1 − σ ) ] + q n f ( x n − τ ) = 0 , where σ and τ are nonnegative constants, { a n }, and { p n , { q n } are nonnegative sequences and f ∈ C(ℜ;ℜ).