Asymptotic Properties of Nonoscillatory Solutions of Third-Order Delay Difference Equations

2018 ◽  
pp. 327-337
Author(s):  
Alina Gleska ◽  
Małgorzata Migda
Keyword(s):  
Difference Equations ◽  
Asymptotic Properties ◽  
Third Order ◽  
Nonoscillatory Solutions ◽  
Delay Difference Equations ◽  
Delay Difference

scholarly journals Nonoscillation of Second-Order Dynamic Equations with Several Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-34 ◽  
Author(s):  
Elena Braverman ◽  
Başak Karpuz
Keyword(s):  
Differential Equations ◽  
Difference Equations ◽  
Delay Differential Equations ◽  
Second Order ◽  
Comparison Theorems ◽  
Nonoscillatory Solutions ◽  
Several Delays ◽  
Delay Differential ◽  
Delay Difference Equations ◽  
Delay Difference

Existence of nonoscillatory solutions for the second-order dynamic equation(A0xΔ)Δ(t)+∑i∈[1,n]ℕAi(t)x(αi(t))=0fort∈[t0,∞)Tis investigated in this paper. The results involve nonoscillation criteria in terms of relevant dynamic and generalized characteristic inequalities, comparison theorems, and explicit nonoscillation and oscillation conditions. This allows to obtain most known nonoscillation results for second-order delay differential equations in the caseA0(t)≡1fort∈[t0,∞)Rand for second-order nondelay difference equations (αi(t)=t+1fort∈[t0,∞)N). Moreover, the general results imply new nonoscillation tests for delay differential equations with arbitraryA0and for second-order delay difference equations. Known nonoscillation results for quantum scales can also be deduced.

scholarly journals Delay difference equations: Coexistence of oscillatory and nonoscillatory solutions

Analysis ◽  
2013 ◽  
Vol 33 (4) ◽  
Author(s):  
Ravi P. Agarwal ◽  
Martin Bohner ◽  
José M. Ferreira ◽  
Sandra Pinelas
Keyword(s):  
Difference Equations ◽  
Nonoscillatory Solutions ◽  
Delay Difference Equations ◽  
Delay Difference

scholarly journals Oscillation of third-order delay difference equations with negative damping term

2018 ◽  
Vol 72 (1) ◽  
pp. 19
Author(s):  
Martin Bohner ◽  
Srinivasan Geetha ◽  
Srinivasan Selvarangam ◽  
Ethiraju Thandapani
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Comparison Theorems ◽  
Asymptotic Behavior Of Solutions ◽  
Delay Difference Equation ◽  
Third Order ◽  
Negative Damping ◽  
The Difference ◽  
Delay Difference Equations ◽  
Delay Difference

The aim of this paper is to investigate the oscillatory and asymptotic behavior of solutions of a third-order delay difference equation. By using comparison theorems, we deduce oscillation of the difference equation from its relation to certain associated first-order delay difference equations or inequalities. Examples are given to illustrate the main results.<br /><br />

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