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.

scholarly journals A Comparison Theorem for Oscillation of the Even-Order Nonlinear Neutral Difference Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Quanxin Zhang
Keyword(s):  
Difference Equation ◽  
Comparison Theorem ◽  
Difference Equations ◽  
Neutral Delay ◽  
Neutral Difference Equation ◽  
Oscillation Criteria ◽  
Even Order ◽  
Delay Difference Equations ◽  
Delay Difference

A comparison theorem on oscillation behavior is firstly established for a class of even-order nonlinear neutral delay difference equations. By using the obtained comparison theorem, two oscillation criteria are derived for the class of even-order nonlinear neutral delay difference equations. Two examples are given to show the effectiveness of the obtained results.

scholarly journals Some Oscillation Results for Even Order Delay Difference Equations with a Sublinear Neutral Term

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Govindasamy Ayyappan ◽  
Gunasekaran Nithyakala
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Delay Difference Equation ◽  
Neutral Delay ◽  
Neutral Term ◽  
All Solutions ◽  
Even Order ◽  
Delay Difference Equations ◽  
Delay Difference

In this paper, some new results are obtained for the even order neutral delay difference equationΔanΔm-1xn+pnxn-kα+qnxn-lβ=0, wherem≥2is an even integer, which ensure that all solutions of the studied equation are oscillatory. Our results extend, include, and correct some of the existing results. Examples are provided to illustrate the importance of the main results.

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 of nonlinear delay difference equations

2001 ◽  
Vol 28 (5) ◽  
pp. 301-306 ◽  
Author(s):  
Jianchu Jiang
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Delay Difference Equation ◽  
Oscillation Criteria ◽  
Delay Difference Equations ◽  
Delay Difference ◽  
Nonlinear Delay

We obtain some oscillation criteria for solutions of the nonlinear delay difference equation of the formxn+1−xn+pn∏j=1mxn−kjαj=0.

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 />

scholarly journals New Oscillation Criteria for Third-Order Nonlinear Mixed Neutral Difference Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Elmetwally Mohammed Elabbasy ◽  
Magdy Yoseph Barsom ◽  
Faisal Saleh AL-dheleai
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Third Order ◽  
Neutral Difference Equation ◽  
Neutral Difference Equations ◽  
Oscillation Criteria

Some new oscillation criteria are established for a third-order nonlinear mixed neutral difference equation. Our results improve and extend some known results in the literature. Several examples are given to illustrate the importance of the results.

scholarly journals Some New Oscillation Criteria for Fourth-Order Nonlinear Delay Difference Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Kandasamy Alagesan ◽  
Subaramaniyam Jaikumar ◽  
Govindasamy Ayyappan
Keyword(s):  
Difference Equation ◽  
Fourth Order ◽  
Difference Equations ◽  
Oscillatory Behavior ◽  
Delay Difference Equation ◽  
Oscillation Criteria ◽  
Delay Difference Equations ◽  
Delay Difference ◽  
Nonlinear Delay

In this paper, the authors studied oscillatory behavior of solutions of fourth-order delay difference equation Δc3nΔc2nΔc1nΔun+pnfun−k=0 under the conditions ∑n=n0∞cin<∞, i=1, 2, 3. New oscillation criteria have been obtained which greatly reduce the number of conditions required for the studied equation. Some examples are presented to show the strength and applicability of the main results.

Oscillation of neutral delay difference equations of second order with positive and negative coefficients

2009 ◽  
Vol 59 (4) ◽  
Author(s):  
Seshadev Padhi ◽  
Chuanxi Qian
Keyword(s):  
Difference Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Neutral Delay ◽  
Neutral Difference Equations ◽  
Positive And Negative Coefficients ◽  
Delay Difference Equations ◽  
Delay Difference

AbstractThis paper is concerned with a class of neutral difference equations of second order with positive and negative coefficients of the forms $$ \Delta ^2 (x_n \pm c_n x_{n - \tau } ) + p_n x_{n - \delta } - q_n x_{n - \sigma } = 0 $$ where τ, δ and σ are nonnegative integers and {p n}, {q n} and {c n} are nonnegative real sequences. Sufficient conditions for oscillation of the equations are obtained.

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