Improved oscillation criteria for second order nonlinear delay difference equations with non-positive neutral term

2016 ◽  
Vol 56 (1) ◽  
pp. 155-165 ◽  
Author(s):  
E. Thandapani ◽  
S. Selvarangam ◽  
R. Rama ◽  
M. Madhan
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Second Order ◽  
Delay Difference Equation ◽  
Oscillation Criteria ◽  
Neutral Term ◽  
Positive Integers ◽  
Delay Difference Equations ◽  
Delay Difference ◽  
Nonlinear Delay

Abstract In this paper, we present some oscillation criteria for second order nonlinear delay difference equation with non-positive neutral term of the form $$\Delta (a_n (\Delta z_n )^\alpha ) + q_n f(x_{n - \sigma } ) = 0,\;\;\;n \ge n_0 > 0,$$ where zn = xn − pnxn−τ, and α is a ratio of odd positive integers. Examples are provided to illustrate the results. The results obtained in this paper improve and complement to some of the existing results.

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 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.

scholarly journals Oscillation theorems for second order difference equations woth negative neutral term

2015 ◽  
Vol 46 (4) ◽  
pp. 441-451 ◽  
Author(s):  
Ethiraju Thandapani ◽  
Devarajulu Seghar ◽  
Sandra Pinelas
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Second Order ◽  
Neutral Difference Equation ◽  
Order Difference ◽  
Oscillation Criteria ◽  
Neutral Term ◽  
Oscillation Theorems ◽  
Positive Integers

In this paper we obtain some new oscillation criteria for the neutral difference equation \begin{equation*} \Delta \Big(a_n (\Delta (x_n-p_n x_{n-k}))\Big)+q_n f(x_{n-l})=0 \end{equation*} where $0\leq p_n\leq p0$ and $l$ and $k$ are positive integers. Examples are presented to illustrate the main results. The results obtained in this paper improve and complement to the existing 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.

Oscillation theorems for second-order delay difference equations with superlinear neutral terms

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Said R. Grace ◽  
John R. Graef
Keyword(s):  
Difference Equations ◽  
Second Order ◽  
New Approach ◽  
Oscillation Criteria ◽  
Neutral Term ◽  
Oscillation Theorems ◽  
Delay Difference Equations ◽  
Delay Difference

Abstract Oscillation criteria for a class of second-order delay difference equations with a superlinear neutral term are established using a new approach. The results improve and significantly simplify the ones reported in the literature.

scholarly journals Oscillation and nonoscillation of nonlinear neutral delay difference equations

2007 ◽  
Vol 38 (4) ◽  
pp. 323-333 ◽  
Author(s):  
E. Thandapani ◽  
P. Mohan Kumar
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Delay Difference Equation ◽  
Neutral Delay ◽  
Delay Difference Equations ◽  
Delay Difference ◽  
Oscillation And Nonoscillation

In this paper, the authors establish some sufficient conditions for oscillation and nonoscillation of the second order nonlinear neutral delay difference equation$$ \Delta^2 (x_n-p_nx_{n-k}) + q_nf(x_{n-\ell}) = 0, ~~n \ge n_0 $$where $ \{p_n\} $ and $ \{q_n\} $ are non-negative sequences with $ 0$

scholarly journals Oscillation Criteria for Generalized Second Kind Sublinear Delay Difference Equations

2018 ◽  
Vol 7 (4.10) ◽  
pp. 340 ◽  
Author(s):  
A. Benevatho Jaison ◽  
SK. Khadar Babu ◽  
V. Chandrasekar
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Nonlinear Difference Equation ◽  
Riccati Transformation ◽  
Transformation Techniques ◽  
Oscillation Criteria ◽  
Positive Integers ◽  
Delay Difference Equations ◽  
Delay Difference

The Using Riccati transformation techniques, we present some new oscillation criteria for generalized second kind nonlinear difference equation when  is a quotient of odd positive integers,    

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