Oscillation of Nonlinear Third-Order Difference Equations with Mixed Neutral Terms

In this paper, new oscillation results for nonlinear third-order difference equations with mixed neutral terms are established. Unlike previously used techniques, which often were based on Riccati transformation and involve limsup or liminf conditions for the oscillation, the main results are obtained by means of a new approach, which is based on a comparison technique. Our new results extend, simplify, and improve existing results in the literature. Two examples with specific values of parameters are offered

Oscillatory behavior of higher order nonlinear difference equations

The authors present some new oscillation criteria for higher order nonlinear difference equations with nonnegative real coefficients of the form   Both of the cases n even and n odd are considered. They give examples to illustrate their results

New oscillation criteria for second order linear difference equations with positive and negative coefficients

AbstractThe oscillation of second order neutral difference equations with positive and negative coefficients of the form Δ2(xn+λanxn−τ)+pnxn−δ−qnxn−σ=0,λ=±1 is investigated. We obtain many new results using the comparison between both first order and second order difference equations. An example is given to show the strength of the obtained results