OSCILLATORY PROPERTIES OF THIRD ORDER NEUTRAL DELAY DIFFERENCE EQUATIONS

2002 ◽  
Vol 35 (2) ◽  
Author(s):  
E. Thandapani ◽  
K. Mahalingam
Keyword(s):  
Difference Equations ◽  
Neutral Delay ◽  
Third Order ◽  
Delay Difference Equations ◽  
Delay Difference ◽  
Oscillatory Properties

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.

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