scholarly journals Comparison Theorems and Oscillation Criteria for Difference Equations

2000 ◽  
Vol 247 (2) ◽  
pp. 397-409 ◽  
Author(s):  
B.G. Zhang ◽  
Yong Zhou
Keyword(s):  
Difference Equations ◽  
Comparison Theorems ◽  
Oscillation Criteria

scholarly journals Some remarks on second order linear difference equations

1998 ◽  
Vol 2 (2) ◽  
pp. 93-97 ◽  
Author(s):  
B. G. Zhang ◽  
Chuan Jun Tian
Keyword(s):  
Difference Equations ◽  
Second Order ◽  
Comparison Theorems ◽  
Linear Difference Equations ◽  
Oscillation Criteria ◽  
Order Linear

We obtain some further results for comparison theorems and oscillation criteria of second order linear difference equations.

scholarly journals Oscillation and comparison theorems for certain neutral difference equations

1992 ◽  
Vol 34 (2) ◽  
pp. 245-256 ◽  
Author(s):  
B. S. Lalli ◽  
B. G. Zhang
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Comparison Theorems ◽  
Neutral Difference Equation ◽  
Neutral Difference Equations ◽  
Oscillation Criteria ◽  
Arbitrary Sign ◽  
Image Position ◽  
Mixed Arguments

AbstractSome comparison theorems and oscillation criteria are established for the neutral difference equationas well as for certain neutral difference equations with coefficients of arbitrary sign. Neutral difference equations with mixed arguments are also considered.

scholarly journals Oscillation Criteria for Third Order Neutral Generalized Difference Equations with Distributed Delay

2019 ◽  
Author(s):  
P.Venkata Mohan Reddy ◽  
M.Maria Susai Manuel ◽  
Adem Kilicman
Keyword(s):  
Difference Equations ◽  
Distributed Delay ◽  
Oscillatory Solution ◽  
Riccati Transformation ◽  
Third Order ◽  
Type Method ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation

This paper aims to investigate the criteria of behaviour of certain type of third order neutral generalized difference equations with distributed delay. With the technique of generalized Riccati transformation and Philos-type method, some oscillation criteria are obtained to ensure convergence and oscillatory solution of suitable example is listed to illustrate the main result.

MODIFIED OSCILLATION CRITERIA OF SECOND-ORDER NEUTRAL DIFFERENCE EQUATIONS

2021 ◽  
Vol 28 (1-2) ◽  
pp. 19-30
Author(s):  
G. CHATZARAKIS G. CHATZARAKIS ◽  
R. KANAGASABAPATHI R. KANAGASABAPATHI ◽  
S. SELVARANGAM S. SELVARANGAM ◽  
E. THANDAPANI E. THANDAPANI
Keyword(s):  
Difference Equations ◽  
Second Order ◽  
Riccati Transformation ◽  
Nonlinear Difference Equations ◽  
Transformation Technique ◽  
Neutral Difference Equations ◽  
Oscillation Criteria ◽  
Neutral Term

In this paper we shall consider a class of second-order nonlinear difference equations with a negative neutral term. Some new oscillation criteria are obtained via Riccati transformation technique. These criteria improve and modify the existing results mentioned in the literature. Some examples are given to show the applicability and significance of the main results.

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.

Sign in / Sign up

Export Citation Format

Share Document