Oscillation of some nonlinear difference equations

We investigate the oscillatory behavior of all solutions of a new class of first order nonlinear neutral difference equations. Several explicit oscillation criteria are established. Our main results are supported by illustrative examples.     

Oscillation of a class of nonlinear neutral difference equations of higher order

Sufficient conditions are obtained under which all solutions of

(∗)     

Oscillation of second-order quasilinear neutral delay difference equations

By using the Riccati transformation and mathematical analytic methods,some sufficient conditions are obtained for oscillation of the second-order quasilinear neutral delay difference equations Δ[r n |Δz n | α-1 Δ z n ] + q n f (x n-σ)=0,where z n=x n + p n x n τ and ∞ Σ n=0 1 /r n 1/α < ∞.     

Oscillation and nonoscillation criteria for second order quasilinear difference equations

New oscillation and nonoscillation theorems are obtained for the second order quasilinear difference equation

Δ(|Δxn−1|^ρ−1Δxn−1)+pn|xn|^ρ−1xn=0,     

On the oscillatory properties of certain fourth order nonlinear difference equations

Some new criteria for the oscillation of fourth order nonlinear difference equations of the form

     

Existence for nonoscillatory solutions of higher-order nonlinear neutral difference equations

In this paper, we consider the following forced higher-order nonlinear neutral difference equation

     

Oscillation criteria for second-order nonlinear neutral delay dynamic equations

In this paper we will establish some oscillation criteria for the second-order nonlinear neutral delay dynamic equation

(r(t)((y(t)+p(t)y(t−τ)Δ⁾γ⁾Δ⁾+f(t,y(t−δ))=0