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.

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 Existence of nonoscillatory solutions to third order nonlinear neutral difference equations

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 4981-4991
Author(s):  
K.S. Vidhyaa ◽  
C. Dharuman ◽  
John Graef ◽  
E. Thandapani
Keyword(s):  
Fixed Point ◽  
Sufficient Conditions ◽  
Delay Difference Equation ◽  
Neutral Delay ◽  
Third Order ◽  
Nonoscillatory Solutions ◽  
Neutral Difference Equations ◽  
Positive And Negative Coefficients ◽  
The Third ◽  
Delay Difference

The authors consider the third order neutral delay difference equation with positive and negative coefficients ?(an?(bn?(xn + pxn-m)))+pnf(xn-k)- qn1(xn-l) = 0, n ? n0, and give some new sufficient conditions for the existence of nonoscillatory solutions. Banach?s fixed point theorem plays a major role in the proofs. Examples are provided to illustrate their main results.

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