Oscillation of solutions of the second-order linear functional-difference equations

2013 ◽  
Vol 65 (2) ◽  
pp. 249-259
Author(s):  
O. V. Karpenko ◽  
V. I. Kravets’ ◽  
O. M. Stanzhyts’kyi
Keyword(s):  
Difference Equations ◽  
Linear Functional ◽  
Second Order ◽  
Functional Difference ◽  
Order Linear ◽  
Functional Difference Equations ◽  
Oscillation Of Solutions

scholarly journals On the Oscillation of Even-Order Half-Linear Functional Difference Equations with Damping Term

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Yaşar Bolat ◽  
Jehad Alzabut
Keyword(s):  
Real Number ◽  
Difference Equations ◽  
Linear Functional ◽  
Oscillatory Behavior ◽  
Functional Difference ◽  
Riccati Transformation ◽  
Damping Term ◽  
Generalized Riccati Transformation ◽  
Even Order ◽  
Functional Difference Equations

We investigate the oscillatory behavior of solutions of themth order half-linear functional difference equations with damping term of the formΔ[pnQ(Δm-1yn)]+qnQ(Δm-1yn)+rnQ(yτn)=0,n≥n0, wheremis even andQ(s)=sα-2s,α>1is a fixed real number. Our main results are obtained via employing the generalized Riccati transformation. We provide two examples to illustrate the effectiveness of the proposed results.

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