By employing the generalized Riccati transformation technique, we will establish some new oscillation criteria for a certain class of third order nonlinear delay difference equations. Our results extend and improve some previously obtained ones. An example is worked out to demonstrate the validity of the proposed results.

https://www.emis.de/journals/EJQTDE/p527.pdf

On the oscillatory behavior for a certain class of third order nonlinear delay difference equations

The third-order nonlinear difference equations @D(p"n@D(r"n@Dx"n))+q"nf(x"n"+"p)=0,p@?{0,1,2},(E"p) where (P"n), (r"n), and (q"n) are sequences of positive real numbers for n @e @?, @? : @? -> @? is a continuous function such that @?(u)u > 0 for u 0, are investigated. All nonoscillatory solutions of these equations are classified according to the sign of their quasidifferences to classes N"i, i = 0, 1, 2, 3, and sufficient conditions ensuring N"i = , i @e {1,2,3} are given. Special attention is paid to equation (E"1) for which the generalized zeros of solutions are studied and an energy function F is introduced. The relation between the class N"0 and solutions for which F"n < 0 for n @e @? is established.

Global asymptotic properties of third-order difference equations

Linear Third-Order Difference Equations: Oscillatory and Asymptotic Behavior

Nonoscillatory solutions of third-order difference equations

This paper is concerned with a class of fourth order nonlinear difference equations. Two types of nonoscillatory solutions will be considered. Relations between these types of solutions and their oscillatory behavior are the main purpose of this paper.

/pdf/oscillation-and-nonoscillation-theorems-for-fourth-order-1314saxszl.pdf

Oscillation and Nonoscillation Theorems for Fourth Order Difference Equations

On etudie l'equation aux differences Δ 3 U n -P n U n+2 =0, ou △ denote l'operation: ΔU n =U n+1 -U n , pour la condition P n >0 pour chaque entier n≥1. On caracterise l'existence de solutions oscillatoires en fonction du comportement des solutions non oscillatoires

/pdf/oscillatory-and-asymptotic-behavior-in-certain-third-order-2yypgzkkpv.pdf

Oscillatory and asymptotic behavior in certain third order difference equations

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Oscillatory and asymptotic behavior in certain third order difference equations