scholarly journals Oscillation criteria for certain third order nonlinear difference equations

2009 ◽  
Vol 3 (1) ◽  
pp. 27-38 ◽  
Author(s):  
Said Grace ◽  
Ravi Agarwal ◽  
John Graef
Keyword(s):  
Difference Equations ◽  
Nonlinear Difference Equations ◽  
Third Order ◽  
Oscillation Criteria ◽  
All Solutions ◽  
New Criteria

Some new criteria for the oscillation of all solutions of third order nonlinear difference equations of the form ? (a(n)(?2 x(n))? + q(n)f (x[g(n)]) = 0 and ? (a(n)(?2 x(n))? = q(n)f (x[g(n)]) + p(n)h(x[?(n)]) ? -1/? with P a (n) < ? are established.

scholarly journals Oscillation criteria of third-order nonlinear neutral delay difference equations with noncanonical operators

2021 ◽  
pp. 11-11
Author(s):  
G. Ayyappan ◽  
G.E. Chatzarakis ◽  
T. Gopal ◽  
E. Thandapani
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Neutral Delay ◽  
Third Order ◽  
Neutral Difference Equations ◽  
Oscillation Criteria ◽  
All Solutions ◽  
Delay Difference Equations ◽  
Delay Difference ◽  
New Criteria

In this paper, we present some new oscillation criteria for nonlinear neutral difference equations of the form ?(b(n)?(a(n)?z(n))) + q(n)x?(?(n)) = 0 where z(n) = x(n) + p(n)x(?(n)),? > 0, b(n) > 0, a(n) > 0, q(n) ? 0 and p(n) > 1. By summation averaging technique, we establish new criteria for the oscillation of all solutions of the studied difference equation above. We present four examples to show the strength of the new obtained results.

Oscillation Criteria for Fourth Order Nonlinear Difference Equations

2007 ◽  
Vol 14 (2) ◽  
pp. 203-222
Author(s):  
Ravi P. Agarwal ◽  
Said R. Grace ◽  
Elvan Akin-Bohner
Keyword(s):  
Difference Equation ◽  
Fourth Order ◽  
Difference Equations ◽  
Nonlinear Difference Equations ◽  
Order Difference ◽  
Oscillation Criteria ◽  
Order Difference Equation ◽  
New Criteria

Abstract Some new criteria for the oscillation of the fourth order difference equation Δ2 (𝑎(𝑛)(Δ2𝑥(𝑛)) α ) + 𝑞(𝑛)𝑓(𝑥(𝑛 + 1)) = 0, where α is the ratio of two positive odd integers are established.

scholarly journals Oscillation Criteria for Third-Order Emden–Fowler Differential Equations with Unbounded Neutral Coefficients

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
George E. Chatzarakis ◽  
Said R. Grace ◽  
Irena Jadlovská ◽  
Tongxing Li ◽  
Ercan Tunç
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Third Order ◽  
Oscillation Criteria ◽  
All Solutions ◽  
New Criteria

New sufficient conditions for the oscillation of all solutions to a class of third-order Emden–Fowler differential equations with unbounded neutral coefficients are established. The criteria obtained essentially improve related results in the literature. In particular, as opposed to known results, new criteria can distinguish solutions of third-order differential equations with different behaviors. Examples are also provided to illustrate the results.

On the oscillation of third order nonlinear difference equations

2009 ◽  
Vol 32 (1) ◽  
pp. 189-203 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Said R. Grace ◽  
Patricia J. Y. Wong
Keyword(s):  
Difference Equations ◽  
Nonlinear Difference Equations ◽  
Third Order

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.

Oscillation criteria for fourth-order functional differential equations

2013 ◽  
Vol 63 (6) ◽  
Author(s):  
Said Grace ◽  
Martin Bohner ◽  
Ailian Liu
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Functional Differential Equations ◽  
Oscillation Criteria ◽  
All Solutions ◽  
Functional Differential ◽  
New Criteria

AbstractSome new criteria for the oscillation of all solutions of certain fourth-order functional differential equations are established.

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